AFM Name______
Applications of Exponential Functions
Practice 1
1. In 1999, the population of a country was 70 million and growing at a rate of 1.9% per year. Assuming the percentage growth rate remains constant, express the population, P, of this country as a function of t, the number of years after 1999.
2. The mass, Q, of a sample of Tritium (a radioactive isotope of Hydrogen), decays at a rate of 5.626% per year, t.
a. Write an equation to describe the decay of a 726 gram sample.
b. When will the sample have decayed to less than 500 grams?
3. In the year 2000, a total of 9.8 million passengers took a cruise vacation. The global cruise industry has been growing at approximately 8% per year for the last decade; assume that this growth rate continues.
a. Write a formula to approximate the number, N, of cruise passengers (in millions) t years after 2000.
b. How many cruise passengers are predicted in the year 2012?
4. Radioactive gallium-67 decays by 1.48% every hour; there are 100 milligrams initially.
a. Find a formula for the amount of gallium-67 remaining after any time.
b. How long will it take for the sample to decay to 20 milligrams?
5. A typical cup of coffee contains 100 mg of caffeine and every hour approximately 16% of the amount of caffeine in the body is metabolized and eliminated.
a. Write a function to model the amount of caffeine in the body as a function of the number of hours since the coffee was consumed.
b. How much caffeine is in the body after 5 hours?
6. The amount (in mg) of a drug in the body t hours after taking a pill is given by .
a. What is the initial dose given?
b. What percent of the drug leaves the body each hour?
c. What is the amount of drug left after 10 hours?
d. After how many hours is there less than 1 milligram left in the body?
7. In 2002, the cost of a train ticket from Boston to New York was $62. Assume that the price rises by 10% per year.
a. Write an equation to model the cost of a ticket as a function of the number of years since 2002.
b. Estimate the cost of a train ticket form Boston to New York in 2010.
c. When will the price exceed $150?
8. You owe $2000 on a credit card. The card charges 1.5% monthly interest on your balance, and requires a minimum monthly payment of 2.5% of your balance. All transactions (payments and interest charges) are recorded at the end of the month. You make only the minimum payment every month and incur no additional debt.
a. Complete the table for a twelve month period.
Month / Balance / Interest / Min Payment0 / $2000.00 / $30.00 / $50.00
1 / $1980.00 / $29.70 / $49.50
2 / $1960.20
3
4
5
6
7
8
9
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b. What is your unpaid balance after one year had passed?
c. At that time, how much of your debt have you paid off?
d. How much money in interest charges have you paid your creditors?