1. Exponential Relations
y = abx
a  b

2. Exponential Relations
y = abx number of periods of growth or decay
a Initial Value
b Growth or Decay Factor

3. Exponential Growth & Decay
Exponential Growth: b >1
y = a(1+r) x
growth factor b = 1 + r  r = % growth as a decimal
(a is still the initial value)
Exponential Decay: b < 1
y = a(1-r) x
growth factor b = 1 - r  r = % decay as a decimal

4. Exponential Growth & Decay Problems
A colony of fruit flies increases by 50% each week. If there are 3 flies around a fruit bowl, how many will there be in 5 weeks?
y = a(1+r) x
y = __________
y = __________ there would be __ flies
y = _________

5. Exponential Growth & Decay Problems
A colony of fruit flies increases by 50% each week. If there are 3 flies around a fruit bowl, how many will there be in 5 weeks?
y = a(1+r) x
y = 3(1+50/100) 5
y = 3(1+0.5) 5 there would be 23 flies
y = 3(1.5) 5
y = 22.78

6. Exponential Growth & Decay Problems
A bacterial population doubles every 20 minutes. If there are 300 bacteria to begin with, how many will there be in 3 hours?
y = a(1+r) x
y = __________
y = _________

7. Exponential Growth & Decay Problems
A bacterial population doubles every 20 minutes. If there are 300 bacteria to begin with, how many will there be in 3 hours?
(Note: x = 3(60÷20) (x = # of hours x # of 20 min periods in 1 hr))
y = a(1+r) x
y = __________
y = _________

8. Exponential Growth & Decay Problems
A bacterial population doubles every 20 minutes. If there are 300 bacteria to begin with, how many will there be in 3 hours?
(Note: x = 3(60÷20) (x = # of hours x # of 20 min periods in 1 hr))
y = a(1+r) x
y = 300(1+100/100) 3(3)
y = 300(2) 9
y =
There would be bacteria

9. Exponential Growth & Decay Problems
If there are 1000 deer in a park and the population decreases at a rate of 3% per year, how many deer will remain in 6 years?
y = a(1- r) x
y = __________
y = _________

10. Exponential Growth & Decay Problems
If there are 1000 deer in a park and the population decreases at a rate of 3% per year, how many deer will remain in 6 years?
y = a(1- r) x
y = 1000(1- 3/100) 6
y = 1000( ) 6
y = 1000(0.97) 6
y = 833
There will be 833 left

11. Exponential Growth & Decay Problems
Caffeine in coffee, tea and many soft drinks goes into your blood stream. It leaves the blood stream at a rate of 13% each hour. What percent of the original amount of caffeine is left in your bloodstream after four hours?
(The initial value is not important. Find the % of “a” that is left)
b = (1 - r) x
b = __________
b = _________

12. Exponential Growth & Decay Problems
Caffeine in coffee, tea and many soft drinks goes into your blood stream. It leaves the blood stream at a rate of 13% each hour. What percent of the original amount of caffeine is left in your bloodstream after four hours?
(The initial value is not important. Find the % of “a” that is left)
b = (1 - r) x
b = (1 – 13/100) 4
b = (1 – 0.13) 4
b = (0.87) 4
b =0 .57 or 57%
57% would be left.

13. Exponential Growth & Decay Problems
A radioactive isotope has a half life of 5 years. A lab has a 24g sample.
How many half lives will have lapsed in 125 years?
___________________________
How much of the sample will be left in 125 years?
y = a(1- r) x
y = __________
y = _________

14. Exponential Growth & Decay Problems
A radioactive isotope has a half life of 5 years. A lab has a 24g sample.
How many half lives will have lapsed in 125 years?
125 ÷ 5 = 25
How much of the sample will be left in 125 years?
y = a(1- r) x
y = __________
y = _________

15. Exponential Growth & Decay Problems
A radioactive isotope has a half life of 5 years. A lab has a 24g sample.
How many half lives will have lapsed in 125 years?
125 ÷ 5 = 25
How much of the sample will be left in 125 years?
y = a(1- r) x
y = 24(1- 0.5) 25
y = 24(0.5) 25
y = 7.15 x 10 -7
There will be 7.15 x 10 -7g

16. In your text do the following:
p200#6 (ans p440),
p182#8 (ans p439),
p187#4 (ans p439),
& Ch 4 Review