Page 1
1.
For the exponential function given, identify A) the initial value and B) the growth
factor.
21 2.5x
y=
2.
Write an equation in the form
x
y C a=
for an exponential function with initial value
46 and growth factor 1.9.
3.
Which equation in the form
x
y C a=
for an exponential function has initial value,
230,000, and growth factor, 1.2?
A)
3.2 26000x
y=
B)
26,000 3.2x
y=
C)
2.6 3.2x
y=
D)
3.2 5.8x
y=
4.
Below are functions that give the population, P, in year, t, for four towns.
Choose the function for the town that has the largest initial population.
A)
440,250 1.38t
P=
B)
587,000 1.13t
P=
C)
880,500 1.19t
P=
D)
3,228,500 1.01t
P=
5.
Below are functions that give the population, P, in year, t, for four towns.
Choose the function for the town that has the smallest growth factor.
A)
330,000 1.21t
P=
B)
20,000 1.2t
P=
C)
630,000 1.11t
P=
D)
780,000 1.1t
P=
6.
Write a function in the form
() x
f x C a=
for an exponential function where
(0) 370,000f=
and for every unit increase in x, the output is multiplied by 1.8.
Page 2
7.
Choose the function of an exponential function where
(0) 4.4f=
and for every unit
increase in x, the output is multiplied by 2.1.
A)
4.4 2.2x
y=
B)
2.2 4.4x
y=
C)
2.2 4.4x
y=
D)
4.4 2.2x
y=
8.
Write a function in the form
() x
f x C a=
for an exponential function with an initial
value of 50 whose output triples for each unit increase of the input.
9.
An outbreak of a flu virus begins with 6 people infected and the number of people
infected increases by a factor of 4.2
each week. Find a formula that gives the number of people infected, I, as a function of
the weeks, w, since the outbreak began.
10.
An outbreak of a flu virus begins with 4 people infected and the number of people
infected increases by a factor of 2
each week.
A) Find a formula that gives the number of people infected, I, as a function of the
weeks, w, since the outbreak began.
B) Use this formula to find the number of people infected after 10 weeks.
11.
When an event happens in a community, news travels fast. Assuming 4 people initially
know the news and the number of people who hear the news increases by a factor of 4.3
each hour, find a formula that gives the number of people who hear the news, N, as a
function of the hours, h, since the event happened.
12.
When an event happens in a community, news travels fast.
A) Assuming 2 people initially know the news and the number of people who hear the
news increases by a factor of 2.8 each hour, find a formula that gives the number of
people who hear the news, N, as a function of the hours, h, since the event happened.
B) Estimate how long, to the nearest hour, it will take for 120 people to hear the news.
13.
An investment is originally worth $19,000 and its worth increases by a factor of 1.008
each month. Find a formula that gives the investment’s worth , W, as a function of the
months, m, since the original investment.
Write your answer in
m
W C a=
form.
Page 3
14.
An investment is originally worth $17,000 and its worth increases by a factor of 1.006
each month.
A) Find a formula that gives the investment’s worth , W, as a function of the months,
m, since the original investment.
B) Use the formula to find the worth of the investment after 16 months.
Round your answer to the nearest cent.
Page 4
15.
Match the function with its graph:
23
x
y=
A)
B)
C)
D)
Page 5
16.
The number of bacteria in a bacterial culture is 59,295 at the end of 5 hours. If the
number of bacteria in the culture increases by a factor of 1.99 every hour, find the
equation to describe the growth of the culture.
Write your answer in
m
y C a=
form. Round each portion of the answer to 2 decimal
places if necessary.
17.
An institution promises that investments in their mutual funds will double every 8 years.
If $5,000 is invested, how much will the investment be worth in 24 years?
18.
A quantity, Q, doubles every 5 years. Write a formula for the quantity of Q where T =
the number of 5 year periods and the amount of the original substance is 580 grams.
19.
How many years does it take for this function to double?
Year
Amount
2000
750
2001
945
2002
1,191
2003
1,500
2004
1,890
2005
2,381
2006
3,000
2007
3,780
Page 6
Answer Key