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Compare linear and exponential growth

p>0

\left(p^{m}\right)^{2 n} \cdot\left(p^{2 m}\right)^{n}=16^{m n}

, then what is the value of

p

8^{\frac{5}{6}}-8^{\frac{1}{2}}=8^{m}

for some value of

m

, what is the value of

m

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1

\newline

\frac{1}{3}

\newline

\frac{1}{2}

\newline

1

\newline

\frac{5}{3}

\frac{\sqrt{8 c^{20}}}{\sqrt{32 c^{4}}}

\newline

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

c \neq 0

\newline

1

\newline

\frac{1}{2} c^{4}

\newline

\frac{1}{2} c^{8}

\newline

\frac{1}{4} c^{16}

\newline

\frac{1}{4} c^{2} \sqrt{c}

2^{m}=x

7^{n}=y

, then which of the following is equivalent to

784^{m n}

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1

\newline

x^{2 m} \cdot y^{4 n}

\newline

x^{2 n} \cdot y^{4 m}

\newline

x^{4 m} \cdot y^{2 n}

\newline

x^{4 n} \cdot y^{2 m}

\frac{2^{z^{2}}}{2^{y^{2}}}=\frac{1}{8}

x+y=-3

, what is the value of

x-y

\left(\frac{9}{8}\right)^{\frac{11}{2}}+\left(\frac{3}{4}\right)^{\frac{17}{2}}

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Which of the following values is equal to the given value?

\newline

1

\newline

\frac{3^{\frac{39}{2}}}{2^{\frac{67}{2}}}

\newline

\left(\frac{15}{8}\right)^{14}

\newline

\frac{3^{11}+3^{\frac{17}{2}}}{2^{\frac{33}{2}}+2^{17}}

\newline

\frac{3^{11} \cdot \sqrt{2}+3^{8} \cdot \sqrt{3}}{2^{17}}

y^{\frac{1}{2}} \cdot \sqrt[3]{16 x^{2} y^{\frac{3}{2}}+8 y^{2}}

\newline

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

y \geq 0

\newline

1

\newline

2 y \sqrt[3]{2 x^{2}+y^{\frac{1}{2}}}

\newline

\sqrt[3]{24 x^{2} y^{\frac{7}{2}}} \cdot y^{\frac{1}{2}}

\newline

y \sqrt[3]{16 x^{2}}+2 y^{\frac{7}{6}}

\newline

\sqrt[3]{16 x^{2} y^{2}+8 y^{\frac{5}{2}}}

\sqrt{x} \cdot \sqrt{\frac{y^{5}}{x^{3}}}

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

x

y

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1

\newline

x^{-2} y^{5}

\newline

x^{-1} y^{\frac{5}{2}}

\newline

x y^{\frac{5}{2}}

\newline

x^{2} y^{5}

\frac{\left(\frac{1}{9}\right)^{124}}{\left(\frac{1}{3}\right)^{72}}

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Which of the following values is equal to the given value?

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1

\newline

3^{-176}

\newline

3^{-52}

\newline

3^{52}

\newline

3^{176}

4^{\frac{1}{5}} \cdot 3^{\frac{2}{5}}=y^{\frac{1}{5}}

\newline

y

satisfies the given equation?

x^{\frac{3}{2}} \cdot\left(\frac{1}{x^{\frac{5}{2}}}\right)^{2}

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

x

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1

\newline

\frac{1}{x^{2}}

\newline

\frac{1}{\sqrt{x^{7}}}

\newline

\frac{1}{\sqrt[7]{x^{2}}}

\newline

\frac{1}{\sqrt[4]{x^{19}}}

2^{5} \cdot\left(\frac{1}{4}\right)^{7}

\newline

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

\newline

1

\newline

2^{-2}

\newline

2^{-4}

\newline

2^{-9}

\newline

2^{10}

\sqrt{y^{3} z} \cdot \sqrt{y^{13} z^{8}}

\newline

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

y

z

\newline

1

\newline

y^{4} z^{3}

\newline

y^{8} z^{4}

\newline

y^{8} z^{4} \sqrt{z}

\newline

y^{15} z^{4} \sqrt{y}

y=g(x)+2

x y

y

1

g

is an exponential function, which of the following could define

g

\newline

1

\newline

g(x)=\left(\frac{1}{4}\right)^{x}-1

\newline

g(x)=2\left(\frac{2}{3}\right) x+1

\newline

g(x)=2^{x}+3

\newline

g(x)=3^{x}-2

f(x)=5(2)^{x}

g(x)=5(b)^{x}

are graphed in the

x y

-plane. If the graph of function

g

is always increasing and

f(x)>g(x)

x>0

, then which of the following could be the value of

b

\newline

1

\newline

0

25

\newline

1

25

\newline

2

\newline

5

An exponential function is graphed in the

x y

-plane. If the graph of the function is always increasing and its

y

(0,6)

, which of the following could be the equation of the function?

\newline

1

\newline

y=6(0.5)^{x}

\newline

y=12(0.5)^{x}

\newline

y=6(2)^{x}+1

\newline

y=4(2)^{x}+2

f(t)=100(1.1)^{3 t}

\newline

Which of the following is an equivalent form of the function

f

in which the exponent is

t

\newline

1

\newline

f(t)=100(1.331)^{t}

\newline

f(t)=100(3.3)^{t}

\newline

f(t)=100(4.1)^{t}

\newline

f(t)=300(1.1)^{t}

f(x)=-2\left(\frac{1}{3}\right)^{x}

g(x)=2\left(\frac{1}{3}\right)^{x}

are graphed in the

x y

(a, b)

is a point on the graph of

f

, then which of the following is a point on the graph of

g

\newline

1

\newline

(a, b)

\newline

(-a, b)

\newline

(a,-b)

\newline

(-a,-b)

y=-3 x

\newline

\frac{y-7}{6}=\frac{3 x^{2}+x-5}{2}

\newline

\left(x_{1}, y_{1}\right)

\left(x_{2}, y_{2}\right)

are the distinct solutions to the system of equations shown, what is the sum of the

y_{1}+y_{2}

f(x)=(x-6)^{2}-9

\newline

Which of the following is an equivalent form of the function

f

in which the zeros of

f

appear as constants or coefficients?

\newline

1

\newline

f(x)=(x-9)(x-6)

\newline

f(x)=(x-9)(x-3)

\newline

f(x)=(x+3)(x+9)

\newline

f(x)=x^{2}-12 x+27

f(x)=-(x+2)^{2}+16

\newline

Which of the following is an equivalent form of the function

f

y

-intercept of the graph of

f

appears as a constant or coefficient?

\newline

1

\newline

f(x)=-(x-6)(x+2)

\newline

f(x)=-(x-2)(x+6)

\newline

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

\newline

f(x)=-x^{2}+4 x+20

f(x)=-x^{2}-14 x-48

\newline

Which of the following is an equivalent form of the function

f

in which the maximum value of

f

appears as a constant or coefficient?

\newline

1

\newline

f(x)=-(x-7)^{2}+1

\newline

f(x)=-(x+7)^{2}+1

\newline

f(x)=-(x+6)(x+8)

\newline

f(x)=-(x-8)(x-6)

f(x)=-(x-4)(x-2)

\newline

Which of the following is an equivalent form of the function

f

in which the maximum value of

f

appears as a constant or coefficient?

\newline

1

\newline

f(x)=-x^{2}+6 x-8

\newline

f(x)=x^{2}-6 x+8

\newline

f(x)=-(x-3)^{2}+1

\newline

f(x)=(x+3)^{2}+1

f(x)=x^{2}-6 x-7

\newline

Which of the following is an equivalent form of the function

f

in which the zeros of

f

appear as constants or coefficients?

\newline

1

\newline

f(x)=(x-7)(x+1)

\newline

f(x)=(x-1)(x+7)

\newline

f(x)=x(x-6)-7

\newline

f(x)=(x-6)^{2}-7

f(x)=(x-4)^{2}-16

\newline

At what values of

x

does the graph of the function intersect the

x

\newline

1

\newline

x=8, x=0

\newline

x=-8, x=0

\newline

x=8, x=-8

\newline

f(x)

does not intersect the

x

f(x)=(x+2)^{2}-16

\newline

At what values of

x

does the graph of the function intersect the

x

\newline

1

\newline

x=2, x=-6

\newline

x=2, x=6

\newline

x=-2, x=-6

\newline

f(x)

does not intersect the

x

f(x)=(x+2)^{2}-64

\newline

At what values of

x

does the graph of the function intersect the

x

\newline

1

\newline

x=6, x=-10

\newline

x=6, x=10

\newline

x=-6, x=-10

\newline

f(x)

does not intersect the

x

f(x)=(x+6)^{2}-16

\newline

At what values of

x

does the graph of the function intersect the

x

\newline

1

\newline

x=-2, x=10

\newline

x=2, x=-10

\newline

x=-2, x=-10

\newline

f(x)

does not intersect the

x

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

g(x)=-(x-4)^{2}+5

are graphed in the same

x y

y=f(x)

y=g(x)

\left(h_{1}, k_{1}\right)

is the vertex of the graph of function

f

\left(h_{2}, k_{2}\right)

is the vertex of the graph of function

g

k_{2}-k_{1}

\newline

1

\newline

-2

\newline

0

\newline

2

\newline

8

f(x)=x^{2}-4 x-1

\newline

Which of the following is an equivalent form of the function

f

in which the minimum value of

f

appears as a constant or coefficient?

\newline

1

\newline

f(x)=-(x-2)^{2}-5

\newline

f(x)=(x-4)(x-1)

\newline

f(x)=(x-2)^{2}-5

\newline

f(x)=x(x-4)-1

f(x)=(x-2)^{2}-9

\newline

At what values of

x

does the graph of the function intersect the

x

\newline

1

\newline

x=-5, x=-1

\newline

x=5, x=1

\newline

x=-5, x=1

\newline

x=5, x=-1

f(t)=80(4)^{t}

\newline

Which of the following is an equivalent form of the function

f

in which the base of the exponent is

2

\newline

1

\newline

f(t)=80(2)^{\frac{t}{2}}

\newline

f(t)=80(2)^{t+2}

\newline

f(t)=80(2)^{2 t}

\newline

f(t)=160(2)^{t}

The exponential function

h

is graphed in the

x y

-plane. If the graph contains the points

(0,18)

(4,3)

, which of the following could be

h

\newline

1

\newline

h(x)=16\left(\frac{1}{2}\right)^{x}+2

\newline

h(x)=16\left(\frac{1}{2}\right)^{x}+3

\newline

h(x)=18\left(\frac{1}{3}\right)^{\frac{x}{2}}

\newline

h(x)=18\left(\frac{1}{2}\right)^{x}-2

y=g(x+5)

x y

-plane passes through the point

(-5,4)

g

is an exponential function, which of the following could define

g

\newline

1

\newline

g(x)=-5(4)^{x}+1

\newline

g(x)=4^{x}

\newline

g(x)=4\left(\frac{4}{5}\right)^{x}

\newline

g(x)=4(2)^{x}-5

y=g(-x)

passes through the point

(2,1)

g

is an exponential function, which of the following could define

g

\newline

1

\newline

g(x)=\left(\frac{1}{2}\right)^{x}-3

\newline

g(x)=16\left(\frac{3}{4}\right)^{x}-8

\newline

g(x)=2^{x}-5

\newline

g(x)=18(3)^{x}-3

R=380(1.08)^{t}

\newline

The given equation models the revenue in thousands of dollars,

R

t

2012

. Of the following, which equation models the revenue of the company

q

2012

\newline

1

\newline

R=380(1.02)^{4 q}

\newline

R=380(1.36)^{q}

\newline

R=380(1.08)^{\frac{q}{4}}

\newline

R=380(1.08)^{4 q}

B(n)=2^{n}

\newline

A binary code word of length

n

0

1

n

digits. For example,

1001

is a binary code word of length

4

. The number of binary code words,

B(n)

n

, is shown. If the length is increased from

n

n+1

, how many more binary code words will there be?

\newline

1

\newline

2

\newline

2^{n}

\newline

2^{n+1}

\newline

4^{n}

S=500(1.02)^{t}

\newline

The given equation models the amount of money in dollars,

S

, in a savings account

t

years after the initial deposit was made. If the interest rate remains constant, which of the following equations models the amount of money in the savings account

d

decades after the initial deposit was made?

\newline

1

\newline

\boldsymbol{S}=500(1.02)^{\frac{d}{10}}

\newline

S=500(1.02)^{10 d}

\newline

S=500(1.22)^{10 d}

\newline

S=500(1.002)^{d}

S=140(0.995)^{m}

\newline

The given equation models the number of subscribers in thousands,

S

, of a newspaper

m

2008

. Which of the following equations models the number of subscribers, in thousands, of the newspaper

y

2008

\newline

1

\newline

S=140(0.942)^{\frac{y}{12}}

\newline

S=140(0.942)^{12 y}

\newline

S=140(0.995)^{\frac{y}{12}}

\newline

S=140(0.995)^{12 y}

x

. Enter the solutions from least to greatest.

\newline

\begin{array}{l} (x-10)^{2}-1=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

(x+2)(x-10)

\newline

Which of the following is equivalent to the given expression?

\newline

1

\newline

2 x^{2}+12 x-20

\newline

2 x^{2}-8 x-20

\newline

x^{2}-20

\newline

x^{2}-8 x-20

\left(2 q^{5}+7 q\right)+\left(5 q^{5}+3 q^{3}\right)

\newline

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

\newline

1

\newline

q\left(7 q^{4}+10\right)

\newline

q\left(7 q^{4}+10 q^{2}\right)

\newline

q\left(2 q^{4}+12 q^{3}+3 q^{2}\right)

\newline

q\left(7 q^{4}+3 q^{2}+7\right)

(x+6)^{2}

\newline

Which of the following is equivalent to the given expression?

\newline

1

\newline

x^{2}+12 x+12

\newline

2 x^{2}+12 x+12

\newline

x^{2}+12 x+36

\newline

2 x^{2}+12

f

f(1)=3

f(3)=7

g

g(3)=9

g(7)=1

. What is the value of

f(g(7))

\newline

1

\newline

1

\newline

3

\newline

7

\newline

9

\begin{array}{l} g(x)=3 x-7 \\ h(x)=2-g(x) \end{array}

\newline

g

h

are defined. What is the value of

h(1)

\newline

1

\newline

6

\newline

1

\newline

-2

\newline

-6

1-9 b^{2}=0

\newline

What are the solutions to the given equation?

\newline

1

\newline

b=-\frac{1}{3}

b=\frac{1}{3}

\newline

b=-\frac{1}{9}

b=\frac{1}{9}

\newline

b=\frac{1}{3}

\newline

b=\frac{1}{9}

(t-10)^{2}-16=0

\newline

What are the solutions to the given equation?

\newline

1

\newline

t=4

t=36

\newline

t=6

t=14

\newline

t=10

t=-16

\newline

t=10

t=16

49 x^{2}-64=0

\newline

What are the solutions to the given equation?

\newline

1

\newline

x=\frac{64}{49}

\newline

x=-\frac{64}{49}

x=\frac{64}{49}

\newline

x=\frac{8}{7}

\newline

x=-\frac{8}{7}

x=\frac{8}{7}

x^{2}+\frac{13}{2} x+\frac{15}{2}=0

\newline

x=a

x=b

are the solutions to the given equation, what is the value of

a b

\newline

1

\newline

-15

\newline

-\frac{15}{2}

\newline

\frac{15}{2}

\newline

\mathbf{1 5}

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