Exponential Models Notes
Name: ____________________________
𝑦 = 𝑎𝑏 𝑥
𝑏 > 1, 𝑔𝑟𝑜𝑤𝑡ℎ
0 < 𝑏 < 1, 𝑑𝑒𝑐𝑎𝑦
Growth:
Decay:
b=1+r
b=1-r
1. Graph 𝑦 = 2𝑥
2. The population in the U.S. in 1994 was 260 million. There is an average rate of increase of .7%
a) Write a function to model this situation:
b) What was the population in 2006?
3. The bear population increases at a rate of 2% a year. There are 1, 573 bears this year.
a) Write a function to model this situation:
b) How many bears will there be in 10 years?
4. Suppose you buy a car for $11, 800. The expected depreciation rate is 20% per year. Estimate the
value of the car after 6 years.
5. The population of a certain animal decreases at a rate of 3.5% per year. Right now there are 80 of that
animal. What is the equation to model this situation?
1
6. Graph 𝑦 = 24(3)𝑥
1
7. Graph 𝑦 = 8(2)𝑥+2 + 3
8. Graph 𝑦 = 2(3)𝑥−1 + 1
Half-Life:
𝑡
1ℎ𝑎𝑙𝑓−𝑙𝑖𝑓𝑒
𝑦= 𝑎
2
9. Mendelevium-257 has a half-life of about 5 hours. I have a 100 mg of a supply of it. How much is
left after 75 hours?
10. Arsenic is used to locate brain tumors. Its half-life is 17.5 days. How much would be remaining of a
90 mg sample after 6 days?