Exponential Functions
Math II Honors
1. In the formula A = P(1 + r)t, P is the principal, r is the annual rate of interest, and A is the amount after t years. An account earning interest at a rate of 4% has a principal of $500,000. If no more deposits or withdrawals are made, about how much money will be in the account after five years?
2. Suppose a ball is dropped from a height of 6 meters and bounces to
90% of its previous height after each bounce. Using the formula
h = 6(0.9)n where n represents the number of bounces and h represents
the maximum height of the ball after the nth bounce, what is the
approximate maximum height of the ball after the 12th bounce?
3. The number of cell phones, y (in thousands), from 1985 to 1995 can
be modeled using the equation y = 0.432(1.55)x, where x is the
number of years after 1985. In what year were there approximately
6 thousand cell phones?
4. A city’s population, P (in thousands), can be modeled by the equation
P = 130(1.03)x, where x is the number of years after January 1, 2000. For
what value of x does the model predict that the population of the city will be
approximately 170,000?
5. A new automobile is purchased for $20,000. If V = 20,000(0.8)x, gives
the car’s value after x years, about how long will it take for the car to
be worth half its purchase price?
6. The value of Mr. Dulaney’s car x years after its purchase is given by the
function V(x) = 15,000(0.87)x . Approximately, what was the value of Mr. Dulaney’s car 5 years after its purchase?
7. Three years ago, Andy invested $5,000 in an account that earns 5% interest
compounded annually. The equation y = 5,000(1.05)t describes the balance
in the account, where t is time in years. Andy made no additional deposits and no withdrawals. How much is in the account now?
8. The function y = 58.7(1.03)t gives a country’s population, y (in millions), where t is the number of years since January 1994. According to this function, what was the approximate population of the country in January 2002?
9. When Robert was born, his grandfather invested $1,000 for Robert’s college education. At an interest rate of 4.5%, compounded annually, approximately how much would Robert have at age 18? (use the formula A = P(1 + r)t ,where P is the principal, r is the interest rate, and t is the time in years)
10. Each year, Cathy invests $1,200 in her account. The account pays an interest rate of 6.3%. The formula to calculate the balance in her account is
B = , where A is the amount invested per year, r is the interest rate, and n is the number of years investing. Approximately how much will Cathy have in her account after 45 years?