Worksheet Exponential Applications

A 15-6

Name ______Date ______Period ______Worksheet – Exponential Applications

1. A radioactive sample decreases by 25% each week. a) If you begin with 5 grams of the substance, give an equation for the amount remaining after t weeks. b) By graphing, find out when 2.5 grams of the substance remains. (This is the half-life of the substance.)

2. Suppose the annual rate of inflation averages 3.8% over the next 10 years. The present cost of an oil change for your car is $23.95. Write a function for the cost of the oil change after t years and approximate the cost 10 years from now.

3. The city of Baltimore has been declining in population for the last 10 years. In the year 2000, the population was 651,000 and declining at a rate of 1.2% per year. a) Give a formula for the population of Baltimore as a function of the years since 2000 (use t = 0 for the year 2000). b) What is the predicted population in the year 2006? (Round to nearest whole number)

4. Radioactive Iodine, I131, used to test for thyroid problems, has a half-life of 8 days. a) If you start with 20 g of radioactive iodine, write a function for the grams of I131 left after t days. b) How much would remain after 5 days? A 15-6

5. Xenon gas, Xe133, is used in medical imaging to study blood flow in the heart and brain. When breathed, it is quickly absorbed into the bloodstream, and is gradually eliminated from the body through exhalation so that there is half as much in the body after 5 minutes. If the patient originally absorbs 3 mL of Xe133, write the function for the amount of Xenon left in the body after t minutes. How much would be left after 12 minutes ?

6. Write the function and find the amounts that result from each investment. a) $1200 invested at 4% compounded quarterly after a period of 3 years.

b) $5000 invested at 8% compounded monthly for 2½ years.

c) $750 invested at 6.25% compounded daily for 5 years.

7. Write the function and find the principal needed to obtain each amount. a) To get $1000 after 2 years at 6% compounded daily.

b) To get $10,000 after 5 years at 7.25% compounded quarterly.

8. Joanne has just inherited an diamond ring appraised at $3000. Suppose diamonds appreciate in value at a rate of 9% annually. a) Write a function for the value of the diamond t years from now.

b) Find A(-10) and explain the meaning of the amount. A 15-6

9. Average salaries of accountants based on the number of years of experience are given in the following table.

Years Experience Salary 0 $42,000 1 $45,000 3 $50,000 5 $60,000 7 $75,000 a) Assuming an exponential model, use regression to find a function for the salary with t years of experience. b) What is the annual rate of change as a percentage?

c) Paste the function into Y= and graph. What would the salary be after 10 years?

d) When could an accountant expect to earn $150,000 according to this model?