Page 1
1.
For an exponential function,
() x
f x C a=
where x is measured in months and
(5) 8f=
and
(11) 22f=
Find A) the 4-month growth factor and B) the monthly growth factor.
Round answers to 2 decimal places.
2.
For an exponential function,
() x
f x C a=
where x is measured in months and
(4) 8f=
and
(9) 29f=
,
which of the following is the monthly growth factor of the function (Rounded to 2
decimal places.)?
A)
4.45
B)
1.16
C)
3.45
D)
0.22
3.
Suppose a town’s population grows from 85,000 to 385,000 over 12 years.
Find A) the 12-year growth factor and B) the annual growth factor.
Round answers to 2 decimal places.
4.
Suppose a town’s population grows from 25,000 to 290,000 over 6 years.
Choose the annual growth factor.
Round answers to 2 decimal places.
A)
265,000
B)
1.50
C)
44,166.67
D)
11.60
5.
Suppose an investment grows from 8,000 to 30,000 over 13 years.
Find A) the 13-year growth factor and B) the annual growth factor.
Round answers to 2 decimal places.
6.
Suppose an investment grows from 9,000 to 48,000 over 9 years.
Choose the annual growth factor.
Round answers to 2 decimal places.
A)
39,000
B)
5.33
C)
4,333.33
D)
1.20
Page 2
7.
Determine whether the data is linear or exponential.
x
y
1
6.48
5
8.82
7
10.28
9
11.99
A)
Exponential
B)
Linear
8.
Determine which data is (roughly) exponential.
A)
x
y
–1
–4.2
1
5.8
2
10.8
6
30.8
B)
x
y
–1
–2.5
1
4.7
2
8.3
6
22.7
C)
x
y
–1
4.1
1
15.6
2
30.4
6
439.8
9.
Write an equation for a function that satisfies these two points:
(0,7)
and
(1,22)
assuming that it is A) a linear function, in the form
y b mx=+
and B) an exponential
function in the form
x
y C a=
.
Round values to 2 decimal places.
10.
Write a function in the form
() x
f x C a=
for an exponential function where
(0) 50f=
and
(1) 95f=
.
11.
Find the growth factor (assuming exponential growth) for a population that grows from
1,100,000 to 1,716,000 in one year.
Page 3
12.
A new cell phone company has 600 subscribers their first year (year 0) and their
business grows to 1,000 subscribers the next year (year 1).
Find a formula for the number of subscribers, C, as a function of the years in business,
y, assuming…
A) linear growth (write your answer in the form
S b my=+
) , and
B) exponential growth (write your answer in the form
y
S C a=
)
Now use these functions to predict how many subscribers they will have in their 20th
year of business (year 19) assuming…
C) linear growth and
D) exponential growth.
Round values to 2 decimal places.
13.
Find the equation of the given function.
x
f(x)
-1
–0.10
0
2.40
1
4.90
2
7.40
Give your answer in
()f x b mx=+
or
() x
f x C a=
form.
14.
Find the equation of the given function.
x
f(x)
-1
2.83
0
3.00
1
3.18
2
3.37
Give your answer in
()f x b mx=+
or
() x
f x C a=
form. Round values to 2 decimal
places.
15.
Choose the function that best matches the description:
when x is 0, y is 5.5, and when x increases 1 unit, y increases 1.42 units
A)
( ) 7 1.22x
fx=
B)
( ) 1.22 7x
fx=
C)
( ) 7 1.22f x x=+
D)
( ) 1.22 7f x x=+
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16.
Choose the function that best matches the description:
when x is 0, y is 2, and when x increases 1 unit, y is multiplied by 1.74
A)
( ) 9 1.92x
fx=
B)
( ) 1.92 9x
fx=
C)
( ) 9 1.92f x x=+
D)
( ) 1.92 9f x x=+
17.
In an effort to control Johne’s disease in dairy cattle, the state of Minnesota set a goal to
reduce the number of cattle with the disease from 15,015 in 1990 to 1,629 in by the year
2000.
A). Assuming a linear model, what would the average rate of change be per year?
B). Assuming an exponential model, what would be the decay factor needed?
Round answers to 3 decimal places if necessary.
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Answer Key