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Fun with Exponential Growth and Decay
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1. At a constant temperature, the atmospheric pressure p in pascals is given by the formula
.001h
, where h is the altitude in meters. (Where appropriate, round all answers to the
nearest tenth of a pascal.)
p  101.3e
a) Find the atmospheric pressure at an altitude of 300 meters.
b) Find the atmospheric pressure at an altitude of 1000 meters.
c) What is the atmospheric pressure at sea level (altitude of 0 meters)?
d) Does this example model exponential growth or exponential decay? Explain how you know and sketch a
graph that might model this relationship.
2. If P dollars are invested into an account that yields an interest rate, r, annually and the interest is
compounded n times a year, then A(t) is the amount in the account after t years. Below is the function that
expresses this:
nt

A(t )  P1 

r

n
Suppose you invest $6000 at an annual interest rate of 2.5%, compounded quarterly. Answer the questions
below. Where appropriate, round to the nearest dollar.
a) How much money would you have after 10 years?
b) How much money would you have after 50 years?
c) About how many years would it take for you to have at least $10,000 in the account?
3. Suppose that, after an initial dose of 60 milligrams, a flea/tick medicine for my greyhound Cassie breaks
down at a rate of 20% per hour in her bloodstream. This means that as each hour passes, 20% of the active
medicine is used.
a) Using a continuous exponential model, write an equation that would predict the amount of medicine in
Cassie’s bloodstream at time, t.
b) How much medicine would Cassie have in her bloodstream after 10 hours? (Round to the nearest tenth
of a milligram.)
4. How long would it take to double your principal (initial amount of money invested in an account) of
$1000 at an annual interest rate of 3% compounded continuously? (Round answer to the nearest year.)
5. The half-life of a radioactive substance is the time it takes for half of the material to decay. Technetium99m is a radioactive isotope that is often used in medicine. After patients ingest the material, the
Technetium-99m emits low-energy gamma rays that can be picked up by a camera, thus helping doctors
discover diseased organs. Technetium-99m has a half-life of 6 hours. This process is modeled by the
equation below, where T is the amount of Technetium-99m in milligrams and x is the number of hours.
1
T  100 
2
1
x
6
a) According to the equation above, how many milligrams of Technetium-99m were ingested at the
beginning of the process?
b) How many milligrams of Technetium-99m would remain after 6 hours?
c) How many milligrams of Technetium-99m would remain in the patient after 24 hours?