Exponential Functions Review
Exponential Functions Review Name_______________________
I. 1. Graph the exponential functions on the calculator. State whether the function is exponential growth or decay; any transformation that occurred and the equation of its horizontal asymptote.
a. y= -2( 2) x
b. f(x)= 2x-2 -3
c. y= 3(.5) x
d. f(x) = 4(1/4) x+3 + 6
e. f(x)= 2ex
II. Exponential models
2. a. A new car costs $32,000. The value decreases by 15% each year. Write an exponential decay model for the car’s value.
b. Use the model to estimate the value after 3 years.
c. Graph the model and predict when the value will be half of the original value.
3.
a. The inflation rate is 3%. The cost of a 40 pound bag of dog food is $31.95. You expect dog food to follow the rate of inflation. Write a model to show the cost of dog food.
a. Graph the model and estimate the year when it would cost about $38.00.
4. You deposit $1500 in a money market account that pays 3.5% annual interest. Find the balance after 1 year if the interest is compounded
a. annually
b. semiannually
c. quarterly
5. Juan and Michelle each have $800. Juan plans to invest $200 for each of the next four years, while Michelle plans to invest all $800 now. Both accounts pay 3% annual interest compounded monthly. Will they have the same amount of money after four years? If not explain.
III. The number e
1. Simplify the expressions
a. (2-2e3) 2 b. –6e * -2e c. -4 -1 d. 12e3
3e2 6 6e 3e
2. Evaluate Using the calculator
a. e3 b. e4 * e-3 c. 4e d. (36e6
3
3. You deposit $1500 in a bank account for 3 years at 2.2% interest. The interest is compounded continuously. How much money will be in the account at the end of the three years?
4. You have a bank account with $1500 as the balance. You deposited $1000 in this bank account. The average interest rate was 3.9% with interest compounded semiannually. How long was the money deposited in this account?
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