ALGEBRA II TRIG - Exponential Growth/Decay Applications
Chapter 4.5 Worksheet 2
General Formulas:
 A = a(b)t
 A(t) = a(1 ± r)t
 A(t) = aekt
Name___________________________
Money/Interest:
 Simple Interest
A = P(1 + r)t
 Compound Interest
𝑟
𝐴 = 𝑃(1 + 𝑛)(𝑛𝑡)
 Compounded
Continuously A =Pe(rt)
Half-Life:
𝑡
1 (ℎ)
𝑎 (2)
−𝑘𝑡

𝐴=

𝐴 = 𝑎𝑒
Doubling:
 A= a(2)t
Application Problems. Solve algebraically.
1.
A certain car depreciates about 15% each year.
a. Write a function to model the depreciation
in value for a car valued at $26,000.
b. How much will the car be worth in 4 years?
c. What is the first year that the value of this car
will be worth less than $10,000?
2.
Kyle estimates that his business is growing at a rate
of 5% per year. His profits in 2010 were $67,000.
a. Estimate his profits for 2014 to the nearest hundred dollars.
b. When will his profits reach $100,000?
c. When will his profits double?
3.
The population of a small farming community is declining at a rate of 7%
per year. The decline can be expressed by the exponential equation
P = C (1 - 0.07) t , where P is the population after t years and C is the current
population. If the population was 8,500 in 2004, when will the population be
less than 6,000?
4.
Lorena deposited $9000 into an account that earns 4.25% interest each year.
a. Write an equation for the amount, A, in the
account after t years if the interest is compounded quarterly.
b. What will the account be worth in 10 years using this method?
c. Write an equation for the amount, A, in the account after t years if it is compounded continuously.
d. In how many years will her account exceed $20,000 using continuous compounding?
e. If she waits for 50 years, how much will be in her account?
5.
A rock that originally had a mass of 1.00 gram of uranium-238 now has only 0.50 grams. How old is the rock if the
half-live of uranium-238 is 4.5 billions of years.
6. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 10 g sample of radon-222 would be left after
15.2 days?
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 2
Name _______________________________________ Date __________________ Class __________________
While John and Cody play their favorite video game,
John drinks 4 cups of coffee and a cola, and Cody
drinks 2 cups of brewed tea and a cup of iced tea.
John recalls reading that up to 300 mg of caffeine is
considered a moderate level of consumption per day.
The rate at which caffeine is eliminated from the
bloodstream is about 15% per hour.
Caffeine Content of Some
Beverages
1. John wants to know how long it will take for the
caffeine in his bloodstream to drop to a moderate
level.
a. How much caffeine did John consume?
Beverage
Caffeine
(mg per serving)
Brewed coffee
103
Brewed tea
36
Iced tea
30
Cola
25
b. Write an equation showing the amount of caffeine
in the bloodstream as a function of time.
c. How long, to the nearest tenth of an hour, will it
take for the caffeine in John’s system to reach
a moderate level?
2. a. Cody thinks that it will take at least 8 hours for the level of caffeine in
John’s system to drop to the same level of caffeine that Cody consumed.
Explain how he can use his graphing calculator to prove that.
b. What equations did Cody enter into
his calculator?
c. Sketch the resulting graph.
Choose the letter for the best answer.
3. About how long would it take for the
level of caffeine in Cody’s system to
drop by a factor of 2?
A 0.2 hour
4. If John drank 6 cups of coffee and a cola,
about how long would it take for the level of
caffeine in his system to drop to a moderate
level?
B 1.6 hours
F 0.5 hour
C 2.7 hours
G 1.6 hours
D 4.3 hours
H 4.7 hours
J 5.3 hours
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 2