Chapter 7 – Exponents Exam Review

1. Write each expression as a single power using only positive exponents.

a) b) c)

d) e) f)

2. The equation represents the population of frogs in a pond, P(n). Where n is the number of years since 1995.

a) List three things you know about the population of frogs just from looking at the equation.

b) How many frogs would you expect to find in the pond in 2009?

3. Jillian just bought a plasma screen television to watch her favourite cricket team. The TV decreases in value exponentially after it is purchased. Its value, V(x) dollars, after x years is given by the equation

a) What does the number 3400 represent?

b) By what percent does the value decrease each year?

c) How much value will be lost on the TV in the sixth year alone?

4. Carbon-14 is used to detect how old fossils are. Carbon-14 decays at a rate of 2% per year.

a) If an organism started with 1000mg of Carbon-14, create a decay formula. Define your variables.

b) Using your formula from a) calculate the amount of Carbon-14 after 43 years.

5. Julia has a major fruit fly infestation in her locker because she accidentally lost track of an orange beneath all of her books. After doing some research on the internet Julia discovered to her horror that the fruit fly population will approximately double every day.

a) If there are 24 fruit flies currently in her locker write an equation to represent this relationship. Define your variables.

b) Use your equation from part a) to determine the number of fruit flies Julia would have after a week.

c) How many fruits flies would have been in there 3 days before the initial count?

Answers:

1.a) b) c) d) e) f)

2.a) decreasing population, 312 frogs in 1995, the rate of decrease is 8% per year b) 97 3.a) initial value of the TV b) 35% c) $138.08

4.a) b) 419.5mg

5.a) b) 3072 c) 3

Chapter 8 - Finance Exam Review

1. After 423 days, an investment earning simple interest at 6.25% had earned $37 in interest. What was the original amount invested?

2. Pete deposits $325 every 3 months for 12 years at 6%/a compounded quarterly. How much will Pete have in his account at the end of the 12 years?

3. Alison invested $2800 into an account that compounded annually. She left the amount in the bank for 15 years. If the investment is worth $4256.78 at maturity determine the annual interest rate.

4. Martha really wants to buy a house in 7 years. In order to obtain a good mortgage rate she needs have saved enough for a down payment of $50,000. She plans to make deposits to a bank account at the end of every month in an account that earns 6.4%/a compounded monthly. Determine the size of the regular deposits Martha must make to achieve her goals.

5. Leanne wins a large amount of money in the lottery. She wants to be able to withdraw regular payments of $2000 every two weeks for the next 30 years. The bank account will earn 4%/a compounded bi-weekly, and the first withdrawal will be made in two weeks. What amount should Leanne deposit in the bank?

6. Liza can start now and invest $200 at the end of every month in an RRSP that pays 5.4% compounded monthly. If she waits 10 years, she could deposit $400 at the end of every month into the same RRSP. If she intends to retire in 30 years, which option will provide the greater amount and by how much?

7. Carter deposits $8900 in an account that pays 6%/a compounded semi-annually. After 4 years, the interest rate changes to 5%/a compounded monthly. Calculate the value of the money 7 months after the change in the interest rate. Hint: A timeline might be helpful.

Answers:

1. $510.83 2. $22608.70 3. 2.83% 4. $474.09 5. $908 086.30

6. $7095.66 7. $11609.92