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Day 5 worked
- 2. Word Problems with Exponentials and Logs
- 3. Exponential Word Problems • Compounded Continuously • Other compounds • Half Life • inc/decreasing and app/depreciation rt PeA = nt n r PA )1( += halflife x inity = 2 1 t rinity )1( ±=
- 4. You have decided to invest $2500 at an 8% annual rate of interest. How much will you have accumulated after 4 years it is compounded: – Annually? – Quarterly? – Daily? – Continuously? nt n r PA )1( += nt n r PA )1( += nt n r PA )1( +=
- 5. You have decided to invest $10,000 at an 6.75% annual rate of interest. How much will you have accumulated after 5 years it is compounded: – Annually? – Quarterly? – Daily? – Continuously? nt n r PA )1( += nt n r PA )1( += nt n r PA )1( +=
- 6. Suppose you invest $1050 at an annual interest rate of 5.5% compounded continuously. How much will you have in the account after 5 years? Suppose you invest $1300 at an annual interest rate of 4.3% compounded continuously. How much will you have in the account after three years? A = Pert
- 7. Interest • An initial investment of $100 is now valued at $149.18. The interest rate is 8% compounded continuously. How long has the money been invested?
- 8. Another Example: • Suppose a $125,000 piece of machinery is depreciating at 8% every year. – How much is it worth after 5 years? – After 7 years? – How long will it take for it to be worth less than $50,000?
- 9. How Long Problems? • Suppose you buy a used car that costs $11,800. The expected depreciation of the car is 20% a year. When will the value be $6,500?
- 10. How Long? • The population of Ramsey City is currently 250 people with a growth rate of 9% a year. How long until the population reaches 5000 people?
- 11. Half Life Problem: A hospital prepares a 100-mg supply of technetium-99mg which has a half-life of 6 hours. Write an exponential function to find the amount of technetium-99mg that remains after 75 hours.
- 12. Another Half-Life: • Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. Write an exponential decay function for a 90-mg sample. Use the function to find the amount remaining after 6 days.
- 13. How long? • Ramsey-26 is a chemical that has a half- life of 3 days. If Amy takes 300 mg of Ramsey-26, then how much is left after 37 days? How long will it take for Amy to only have 5 mgs left in her body?
- 14. Homework • Pg. 342 (3, 11, 17, 21-29 odd) • Worksheet • Sticker worksheet