Resources

Resources

Compare linear and exponential growth

\left(v+\frac{1}{5}\right)^{2}-9=0

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What is the sum of the solutions to the given equation?

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1

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-\frac{3}{5}

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-\frac{2}{5}

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-\frac{1}{5}

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0

(x+3)^{2}-4=0

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What are the solutions to the given equation?

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1

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x=1, x=5

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x=1, x=-5

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x=-1, x=5

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x=-1, x=-5

x^{2}-13 x+30=0

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What are the solutions to the given equation?

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1

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x=-15

x=2

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x=-10

x=-3

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x=3

x=10

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x=-2

x=15

(x-3)^{2}

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Which of the following is equivalent to the given expression?

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1

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x^{2}+6 x+9

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x^{2}-6

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2 x^{2}+9

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x^{2}-6 x+9

f=12 g h+15 g

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The equation gives the quantity

f

in terms of the quantities

g

h

. Which of the following equations correctly expresses

g

f

h

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1

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g=\frac{f}{12 h+15}

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g=\frac{f}{12 h-15}

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g=\frac{f-15}{12 h}

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g=\frac{f}{27 h}

j=\frac{m}{c} \cdot 78

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Which of the following equations correctly expresses

c

j

m

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1

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c=\frac{m}{j} \cdot 78

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c=\frac{m}{78 \cdot j}

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c=\frac{j}{m} \cdot 78

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c=\frac{j}{78 \cdot m}

A=\frac{1}{2}\left(b_{1}+b_{2}\right) h

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A

, of a trapezoid that has a height,

h

b_{1}

b_{2}

, can be found by using the given equation. Which of the following correctly shows the trapezoid's height in terms of its area and

2

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1

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h=\frac{A}{2}\left(b_{1}+b_{2}\right)

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h=\frac{2}{A\left(b_{1}+b_{2}\right)}

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h=\frac{A}{2\left(b_{1}+b_{2}\right)}

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h=\frac{2 A}{\left(b_{1}+b_{2}\right)}

l=\frac{125}{m}+50 n

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The equation gives the quantity

l

in terms of the quantities

m

n

. Which of the following equations correctly expresses

n

l

m

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1

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n=\frac{l-125}{50 m}

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n=\frac{l}{50}-\frac{125}{m}

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n=\frac{l}{50}-\frac{5}{2 m}

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n=\frac{5}{2 m}-\frac{l}{50}

A circle graphed in the

x y

-plane has its center at

(0,15)

(3,2)

lies on the circle, which of the following is an equation of the circle?

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1

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(x-15)^{2}+y^{2}=178

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(x-15)^{2}+y^{2}=\sqrt{178}

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x^{2}+(y-15)^{2}=178

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x^{2}+(y-15)^{2}=\sqrt{178}

What is the value of

\sin \left(60^{\circ}\right) ?

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1

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-\frac{\sqrt{3}}{2}

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-\frac{1}{2}

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\frac{1}{2}

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\frac{\sqrt{3}}{2}

y=\left(x^{2}-1\right)(x+4)-9

, what is the value of

y

x=1

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1

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-9

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-5

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-4

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0

f(x)=x^{3}-4 x^{2}+3 x-12

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f

x-4

f

, what is the value of

f(4) ?

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1

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-12

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0

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12

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64

f(x)=2 x^{3}-2 x^{2}+18 x-18

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f

x-1

f

, what is the value of

f(1)

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1

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-40

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-18

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0

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1

f(x)=3 x^{3}-7 x^{2}+9 x-4

, what is the value of

f(0)

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1

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-4

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0

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1

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3

-20 x^{2}+25 x^{2} y-40 x=-5 x(4

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In the given equation,

c

is a positive constant. What is the value of

c

[(9 f+9)+(9 f+9+1)] \cdot f

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Which of the following expressions is equivalent to the given expression?

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1

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18\left(f^{2}+f\right)

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18 f^{2}+18 f+1

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18\left(f^{2}+f+1\right)

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18 f^{2}+19 f

-y^{2}(6 x-y)

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Which of the following is equivalent to the given expression?

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1

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-6 x^{3}+x^{2} y

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-6 x^{2} y+y^{3}

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-6 x y^{2}+y^{3}

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6 x y^{2}-y^{3}

x^{2}+5 x-3 x-2 x-100

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Which of the follow expressions is equivalent to the given expression?

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1

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6 x^{2}-2 x-100

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6 x^{2}-5 x-100

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x^{2}-10 x-100

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x^{2}-100

Which of the following is equivalent to

x(x-1)

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1

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2 x-1

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x^{2}-x

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x^{2}-1

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2 x^{2}-x

\left(a^{3}\right)^{3} \cdot a^{-9}

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Which of the following expressions is equivalent to the given expression for all

a \neq 0

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1

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0

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1

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a^{3}

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a^{18}

\frac{a^{5} l^{2}}{3} \cdot \frac{b}{a^{2}}

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Which expression is equivalent to the product for all

a>0

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1

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\frac{b l^{2}}{3 a^{3}}

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\frac{a^{7} l^{2}}{3 b}

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\frac{b l^{2}}{3}

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\frac{a^{3} b l^{2}}{3}

Which of the following is equivalent to

\left(2^{x}\right)^{3}

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1

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6^{x}

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6^{x^{3}}

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8^{x}

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8^{3 x}

Which of the following is equivalent to

\left(3^{a}\right)^{2}

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1

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9^{2 a}

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9^{a}

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6^{a}

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6^{2 a}

\frac{a^{8} b^{-2}}{a^{2} b^{10}}

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Which of the following is equivalent to the given expression for

a, b \neq 0

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1

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a^{4} b^{-5}

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a^{6} b^{12}

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\frac{a^{4}}{b^{-5}}

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\frac{a^{6}}{b^{12}}

\left(a^{m}\right)^{n} \cdot a^{m n}

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Which of the following is equivalent to the given expression?

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1

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2 a^{m n}

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a^{2 m n}

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a^{m^{2} n^{2}}

\newline

a^{m^{n}+m n}

\left(\frac{1}{2}\right)^{-2}+3^{0}

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What is the value of the given expression?

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1

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\frac{3}{4}

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\frac{5}{4}

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4

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5

b^{3} \cdot\left(b^{4}\right)^{2}=b^{x}

, what is the value of

x

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1

\newline

9

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11

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18

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19

\left(2 b^{-5}\right)^{3}

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Which of the following is equivalent to the given expression for all

b \neq 0

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1

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\frac{2}{b^{15}}

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\frac{8}{b^{15}}

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\frac{1}{2 b^{15}}

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\frac{1}{8 b^{15}}

h(t)=88-37(0.85)^{t}

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A human child grows rapidly in the first

36

months after birth. The given function models

h

, the child's height in centimeters,

t

months after birth for

0 \leq t \leq 36

36

72

months after birth, the child grows at an average rate of

0

5

centimeter per month. Approximately how many more centimeters does the child grow in their first

36

months after birth compared to their second

36

36

72

months) after birth?

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1

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19

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37

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51

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88

T(t)=25+65 \cdot(0.78)^{t}

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A pot of soup is heated and then left to cool in a room with a constant temperature. The equation gives the temperature of the soup,

T(t)

, in degrees Celsius

\left({ }^{\circ} \mathrm{C}\right), t

minutes after it is heated. What is the initial temperature of the soup before it begins to cool?

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1

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25^{\circ} \mathrm{C}

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65^{\circ} \mathrm{C}

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78^{\circ} \mathrm{C}

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90^{\circ} \mathrm{C}

f(m)=500\left(\frac{1}{2}\right)^{\frac{m}{20}}

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The function models

f

, the amount of a particular medicine in milligrams in a patient's bloodstream,

m

minutes after the medicine is fully absorbed. Based on the function, how many minutes does it take for the amount of medicine in the patient's bloodstream to reduce by half?

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1

\newline

\frac{1}{2}

\newline

\mathbf{1 0}

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20

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\mathbf{2 5 0}

24

30 \%

25

milligram dose of a new antibiotic remains in the body. Which of the following functions,

M

, models the amount of the antibiotic (in milligrams) that remains in the body after

h

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1

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M(h)=30 \cdot(0.3)^{\frac{h}{24}}

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M(h)=25 \cdot(0.3)^{\frac{h}{24}}

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M(h)=25 \cdot(0.3)^{h}

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M(h)=25 \cdot(0.7)^{\frac{h}{24}}

P(t)=20(0.95)^{t}

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The function models

P

, the population of Leetown in thousands,

t

2007

. What was the population of Leetown in

2007

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1

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5

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19

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20

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95

f(x)=10(1.25)^{x}

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The function models

f

, the price of a rare trading card in dollars

x

years after its initial release in

1993

. Based on the model, what is the price of the trading card

20

years after its initial release?

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1

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\$ 15.63

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\$ 16.39

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\$ 93.13

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\$ 867.36

h(t)=56-4.9 t^{2}

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The function models

h

, the height of a flower pot in meters,

t

seconds after it falls from a fourth floor balcony. What is the height of the flower pot, in meters,

3

seconds after it falls?

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1

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51

1

\newline

44

1

\newline

36

4

\newline

11

9

h(t)=-4.9 t^{2}+12 t+0.5

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The function models

h

, the height of a soccer ball in meters

t

seconds after it is kicked. About what is the height, in meters, of the soccer ball

2

3

seconds after it is kicked?

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1

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1

7

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2

2

\newline

4

9

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16

8

y=3 x-15

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y=x^{2}-2 x-15

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(x, y)

is a solution to the system of equations and

x>0

, what is the value of

x

\newline

1

\newline

1

\newline

5

\newline

6

\newline

15

j^{3}+3 j^{2} k+3 j k^{2}+k^{3}

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Which of the following is equivalent to the given expression?

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1

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j^{3}+3(j k)^{2}+k^{3}

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j^{3}+6(j k)^{2}+k^{3}

\newline

j^{3}+3 j k(j+k)+k^{3}

\newline

j^{3}+6 j k(j+k)+k^{3}

\frac{x^{2}}{x-2}+\frac{4}{2-x}

\newline

Which of the following is equivalent to the given expression shown for

x \neq 2

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1

\newline

x+2

\newline

x-2

\newline

\frac{x^{2}-4}{2-x}

\newline

\frac{x^{2}+4}{x-2}

\frac{3}{14 y}+\frac{y}{14}

\newline

Which expression is equivalent to the sum for

y \neq 0

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1

\newline

\frac{3+y}{14 y+14}

\newline

\frac{4}{14}

\newline

\frac{3+y}{14}

\newline

\frac{3+y^{2}}{14 y}

\frac{5 x}{6 y} \cdot \frac{3}{10 y}

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Which expression is equivalent to the product for all

y>0

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1

\newline

\frac{x}{2}

\newline

\frac{25 x}{9}

\newline

\frac{x}{2 y^{2}}

\newline

\frac{x}{4 y^{2}}

\frac{3 g^{2}+12 g}{g+7} \cdot \frac{4}{8 g^{2}}

\newline

Which expression is equivalent to the product for all

g>0

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1

\newline

\frac{3 g+48}{g^{2}+56 g}

\newline

\frac{12 g+12}{8 g^{2}+7 g}

\newline

\frac{3 g+12}{2 g^{2}+14 g}

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\frac{3+12 g}{2 g+14}

\$ 450

she earned from her summer job into an account and will use it to pay for school expenses. She withdraws

10 \%

of the remaining balance each month to pay for part of her living expenses. Which of the following functions models the balance,

B

, of Wyatt's money (in dollars)

t

months after she started school?

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1

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B(t)=450 \cdot(1.1)^{t}

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B(t)=450 \cdot(0.9)^{t}

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B(t)=450+1.1 t

\newline

B(t)=450-0.9 t

Under ideal conditions, Lemna minor (common duckweed) is a fastgrowing fern that can double its area every

2

days. Assume the growth is unrestricted, and that the duckweed initially covers

10

square centimeters

\left(\mathrm{cm}^{2}\right)

in area. Which of the following functions,

F

, models the area (in

\mathrm{cm}^{2}

) the duckweed covers after

d

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1

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F(d)=10(0.5)^{\frac{d}{2}}

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F(d)=2(10)^{d}

\newline

F(d)=10(2)^{d}

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F(d)=10(2)^{\frac{d}{2}}

Rocio drops a ball from a height of

4

meters. Rocio observes that each time the ball bounces, it reaches a peak height which is

79 \%

of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height,

h

, in meters, after

b

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1

\newline

h=4 \cdot 0.79^{(b-1)}

\newline

h=4 \cdot 0.79^{b}

\newline

h=4-0.79 \cdot b^{2}

\newline

h=4 \cdot\left(1-0.79 \cdot b^{2}\right)

A(q)=86(0.9)^{\frac{q}{4}}

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The function models

A

, the number of active players, in thousands, of a mobile game

q

quarter years after

2018

. Based on the function, how many quarter years does it take for the number of active players to decreases by

10 \%

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1

\newline

0

1

\newline

0

225

\newline

0

9

\newline

4

P(t)=1,800(1.004)^{t}

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The function models

P

, the amount of money, in dollars, in Yara's savings account

t

years after she opened the account with an initial deposit of

\$ 1,800

. How much money is in Yara's account

5

years after her initial deposit if she makes no deposits or withdraws in that time?

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1

\newline

\$ 1,836.29

\newline

\$ 1,873.31

\newline

\$ 2,189.98

\newline

\$ 9,036

Poultry should be cooked to a temperature of

75^{\circ} \mathrm{C}

. A chicken is removed from the oven and left to rest in a room that is at a constant temperature of

22^{\circ} \mathrm{C}

. The temperature of the chicken

t

hours after it is removed from the oven is given by the exponential function:

\newline

T(t)=22+53(0.74)^{t}

\newline

What is the approximate temperature of the chicken after

2

\newline

1

\newline

22^{\circ} \mathrm{C}

\newline

51^{\circ} \mathrm{C}

\newline

74^{\circ} \mathrm{C}

\newline

75^{\circ} \mathrm{C}

p(t)=80(1.05)^{t}

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The function models

p

, the population, in thousands, of City

X

t

2000

. Based on the model, what is the approximate population, in thousands, of City

X

2010

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1

\newline

88

\newline

130

\newline

212

\newline

840

P(t)=30(2)^{\frac{t}{18}}

\newline

The function models

P

, the amount of bacteria, in colony-forming units, in a bacteria culture after

t

minutes of growth. How many colonyforming units of bacteria are in the bacteria culture after

90

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1

\newline

3 \times 10^{2}

\newline

9.6 \times 10^{2}

\newline

5.4 \times 10^{3}

\newline

2.43 \times 10^{7}

...

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