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1.
Determine whether the function represents exponential growth or decay.
26 0.1x
y=
A)
Growth
B)
Decay
2.
Determine whether the function represents exponential growth or decay.
30 1.1 x
y−
=
A)
Decay
B)
Growth
3.
For the exponential function given, identify A) the initial value and B) the growth or
decay factor.
32,000 0.3x
y=
4.
Write an equation in the form
x
y C a=
for an exponential function with initial value
3,700 and growth factor 1.9.
5.
Write a function in the form
() x
f x C a=
for an exponential function where
(0) 43f=
and for every unit increase in x, the output is multiplied by 0.3.
6.
Write an equation for an exponential function (in the form
x
y C a=
) that satisfies these
two points:
(0,9)
and
(1,2.7)
Round values to 2 decimal places.
7.
Write a function in the form
() x
f x C a=
for an exponential function where
(0) 450f=
and
(1) 1,530f=
.
8.
Find the growth/decay factor (assuming exponential growth/decay) for a population that
decreases from 29,000,000 to 24,940,000 in one year.
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9.
Find the formula of the given exponential function.
x
f(x)
-1
5.12
0
6.50
1
8.26
2
10.48
Give your answer in
() x
f x C a=
form. Round values to 2 decimal places.
10.
A piece of equipment is originally worth $18,000 and its worth decreases by a factor of
0.6 each year.
A) Find a formula that gives the equipment’s value , V, as a function of the years, y,
since its purchase.
B) Use the formula to find the worth of the equipment after 3 years.
Round your answer to the nearest cent.
11.
Find an exponential function where
(0) 13f=
and
(9) 47f=
Write your answer in
() x
f x C a=
form and round values to 2 decimal places.
12.
The half-life of Beryllium 11 is 13.81 seconds. If a sample initially contains 2,800
atoms, create a formula to represent the number of atoms, A, in the sample after T
intervals of 13.81 seconds.
13.
The half-life of Flourine 20 is 11 seconds. If a sample initially contains 2,200 atoms,
how long would it take for the sample to decay to 275 atoms?
14.
The half-life of Fluorine 18 is 1.82 hours. If a sample initially contains 6,400 atoms,
how many atoms will be left after 3.64 hours? Round the answer to the nearest whole
number if necesasry.
15.
The half-life of penicillin in a beef cow is approximately 30 hours. If a beef cow is
administered 45 mL of penicillin, how long will it take for the animal to reach the
acceptable level for butchering of 0.5 mL? (Round your answer to the nearest tenth of
an hour.)
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16.
The half-life of penicillin in a beef cow is approximately 30 hours. If the acceptable
level for butchering of 0.5 mL, and the beef cow is administered 25 mL of penicillin,
will it be at an acceptable level to butcher after 7 days? (Answer “Yes” or “No”.)
17.
If the half-life of francium is 21 minutes, how long would it take for a 2,000 gram
sample to decay to less than 60 grams? (Round the answer to the nearest minute.)
18.
If the half-life of francium is 21 minutes, how much of a 4,000 gram sample would be
left after 20 minutes? (Round the answer to the nearest gram.)
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Answer Key