Homework Questions

Word Problems with Exponentials and Logs

Exponential Word Problems

• Compounded Continuously

• Other compounds

• Half Life

• inc/decreasing and app/depreciation

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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?

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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?

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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?

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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?

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?

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?

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?

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.

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.

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?

Homework

• Pg. 342 (3, 11, 17, 21-29 odd)• Worksheet

• Sticker worksheet