Exponential Relations y = abx a  b

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

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

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 = _________

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

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 = _________

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 = _________

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 = 153600 There would be 153600 bacteria

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 = _________

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(1- 0.03) 6 y = 1000(0.97) 6 y = 833 There will be 833 left

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 = _________

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.

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 = _________

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 = _________

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

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