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Math Problems
Algebra 1
Write linear and exponential functions: word problems
Use a graphing calculator and the following scenario.
\newline
The population
P
P
P
of a fish farm in
t
t
t
years is modeled by the equation
P
(
t
)
=
1700
1
+
9
e
−
0.6
t
P(t)=\frac{1700}{1+9 e^{-0.6 t}}
P
(
t
)
=
1
+
9
e
−
0.6
t
1700
.
\newline
To the nearest tenth, how long will it take for the population to reach
900
900
900
?
\newline
□
\square
□
yr
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A town has a population of
1.025
×
1
0
5
1.025 \times 10^{5}
1.025
×
1
0
5
and shrinks at a rate of
5
%
5 \%
5%
every year. Which equation represents the town's population after
6
6
6
years?
\newline
P
=
(
1.025
×
1
0
5
)
(
1
−
0.05
)
(
1
−
0.05
)
(
1
−
0.05
)
P=\left(1.025 \times 10^{5}\right)(1-0.05)(1-0.05)(1-0.05)
P
=
(
1.025
×
1
0
5
)
(
1
−
0.05
)
(
1
−
0.05
)
(
1
−
0.05
)
\newline
P
=
(
1.025
×
1
0
5
)
(
0.05
)
6
P=\left(1.025 \times 10^{5}\right)(0.05)^{6}
P
=
(
1.025
×
1
0
5
)
(
0.05
)
6
\newline
P
=
(
1.025
×
1
0
5
)
(
0.95
)
6
P=\left(1.025 \times 10^{5}\right)(0.95)^{6}
P
=
(
1.025
×
1
0
5
)
(
0.95
)
6
\newline
P
=
(
1.025
×
1
0
5
)
(
1
−
0.5
)
6
P=\left(1.025 \times 10^{5}\right)(1-0.5)^{6}
P
=
(
1.025
×
1
0
5
)
(
1
−
0.5
)
6
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Every year
39
39
39
million cars cross the Golden Gate Bridge in San Francisco.
\newline
Which kind of function best models the relationship between time and the cumulative number of cars that have crossed the Golden Gate Bridge?
\newline
Choose
1
1
1
answer:
\newline
A) Linear
\newline
B) Exponential
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When studying a new antiviral drug, researchers found that the drug concentration in a patient's bloodstream halves every
2
2
2
hours. Which of the following best describes how the drug concentration changes as time elapses?
\newline
Choose
1
1
1
answer:
\newline
(A) Linear increase
\newline
(B) Linear decrease
\newline
(C) Exponential increase
\newline
(D) Exponential decrease
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The highest recorded wind speed not associated with a tornado was recorded at Barrows Island, Australia, in the year
1996
1996
1996
. The wind gust of
220
220
220
knots
(
k
n
)
(\mathrm{kn})
(
kn
)
toppled the previous record held at Mount Washington. What was the wind speed in miles per hour
\newline
(
m
i
h
r
)
?
(
1
k
n
=
1.15
m
i
h
r
)
\begin{array}{l} \left(\frac{\mathrm{mi}}{\mathrm{hr}}\right) ? \\ \left(1 \mathrm{kn}=1.15 \frac{\mathrm{mi}}{\mathrm{hr}}\right) \end{array}
(
hr
mi
)
?
(
1
kn
=
1.15
hr
mi
)
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It always takes Zach approximately
5
5
5
minutes longer to arrive than he says. If Zach says he will arrive in
x
x
x
minutes, which of the following functions correctly models the approximate number of minutes it actually takes Zach to arrive?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
x
)
=
5
x
f(x)=5 x
f
(
x
)
=
5
x
\newline
(B)
f
(
x
)
=
x
−
5
f(x)=x-5
f
(
x
)
=
x
−
5
\newline
(C)
f
(
x
)
=
x
+
5
f(x)=x+5
f
(
x
)
=
x
+
5
\newline
(D)
f
(
x
)
=
5
−
x
f(x)=5-x
f
(
x
)
=
5
−
x
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P
(
t
)
=
25
(
2
)
t
1.06
P(t)=25(2)^{\frac{t}{1.06}}
P
(
t
)
=
25
(
2
)
1.06
t
\newline
The number of yeast cells,
P
(
t
)
P(t)
P
(
t
)
, in a culture after
t
t
t
days is modeled by the equation shown. After how many days will the population double in size?
\newline
(Round your answer to the nearest hundredth.)
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Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits
x
x
x
days to pick up the motorcycle.
\newline
Write an equation for the function. If it is linear, write it in the form
g
(
x
)
=
m
x
+
b
g(x) = mx + b
g
(
x
)
=
m
x
+
b
. If it is exponential, write it in the form
g
(
x
)
=
a
(
b
)
x
g(x) = a(b)^x
g
(
x
)
=
a
(
b
)
x
.
\newline
g
(
x
)
=
‾
g(x) = \underline{\hspace{3em}}
g
(
x
)
=
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