Exercise Set 4.5: Applications of Exponential Functions Answer the following. Compound interest is calculated by the following formula:
r⎞ ⎛ A(t ) = P0 ⎜1 + ⎟ ⎝ n⎠
nt
1. If you invest $25,000 in an account that gets 12% annual interest compounded quarterly, how much would you have in 10 years? 2. If you invested a penny on Jan 1, 1776 at 10% interest compounded daily, how much would you have on Jan 1, 2011? 3. An amount of $1,000 is invested in an account that pays 4% annually. Assume that no deposits or withdraws are made. How much is in the account after 6 years if the money is a) compounded monthly, b) compounded daily? 4. If you invest $3000 in a savings account that earns 4% compounded annually, how much is the investment worth after 7 years? 5. If you purchase a Saab for $48,000, the value of the car depreciates by 18% each year. How much will the car be worth after 5 years? 6. If you purchase a Mercedes Benz for $50,000, the value of the car depreciates by 20% each year. How much will the car be worth after 4 years?
Exponential Growth is calculated by the following formula: t r P(t ) = P0 (b ) 7. The bacterium E. coli doubles every 20 minutes. How many bacteria would there be after 4 hours if we started with a sample of 100 bacteria? 8. The bacterium Staphylococcus aureu doubles every 20 minutes. How many bacteria would there be after 6 hours if we started with a sample of 200 bacteria? 9. A certain bacteria culture triples every 30 minutes. The initial population of the bacteria is 60 cells. How many bacteria will there be after 10 hours? 10. A certain bacteria culture triples every 30 minutes. The initial population of the bacteria is 80 cells. How many bacteria will there be after 16 hours? Exponential Decay is calculated by the following formula: t r P(t ) = P0 (d ) 11. The half-life of bismuth-210 is 5 days. How much of an 800-mg sample would be left after 30 days? 12. The half-life of cesium-137 is 30 years. Suppose we have a 100-mg sample. How much of the sample will remain after 120 years? 13. The half-life of cobalt-60 is 5.24 years. How much of a 100-mg sample would be left after 20 years? 14. The half-life of carbon-14 is 5,730 years. How much of a 50 gram sample would be left after 15,000 years?
