Exponential Models Worksheet with Answers – Algebra 2 (Free PDF)

Problem 1 Growth or decay ★★★

For each function, state whether it models growth or decay and give the percent change per period.

1. y = 250(1.04)^t
2. y = 90(0.85)^t
3. y = 3 · 2^t
4. y = 1,200(0.97)^t

Problem 2 A growing town ★★★

A town of 8,400 people grows 3% per year. Write a model for the population after t years and find the population after 5 years, rounded to the nearest person.

Problem 3 A depreciating car ★★★

A $31,500 pickup truck loses 11% of its value each year. Write a model for its value after t years and find the value after 3 years.

Problem 4 Reading an exponential graph ★★★

The graph of y = 200(1.25)^t is shown. Identify the initial value and the growth factor, then find y when t = 2 and t = 3.

Problem 5 Evaluating powers of e ★★★

Use a calculator to evaluate each expression to three decimal places.

1. e^0.5
2. e⁻¹
3. e^2.3

Problem 6 Annual compounding ★★★

A deposit of $2,500 earns 4.5% interest compounded annually. Find the balance after 6 years.

Problem 7 Monthly compounding ★★★

A deposit of $4,000 earns 3.6% interest compounded monthly. Find the balance after 5 years.

Problem 8 Continuous compounding ★★★

A deposit of $1,500 earns 5% interest compounded continuously. Find the balance after 8 years.

Problem 9 Comparing compounding frequencies ★★★

Find the value of $1,000 at 6% after 10 years when it is compounded annually, quarterly, monthly, and continuously. The figure shows two of the graphs.

Problem 10 Interpreting parameters ★★★

The value of a delivery van is modeled by V(t) = 15,000(0.9)^t, where t is in years. State what 15,000 and 0.9 mean, and find the value after 2 years.

Problem 11 Half-life ★★★

A 80-milligram sample of a medicine has a half-life of 6 days. Write the model N(t) = 80(1/2)^t/6, then find the amount remaining after 18 days and after 3 days.

Problem 12 Doubling time ★★★

A bacteria culture starts with 500 cells and doubles every 3 hours. Write a model, then find the number of cells after 12 hours and after 5 hours.

Problem 13 Changing the time unit ★★★

A quantity is modeled by y = 200(1.5)^t/2, where t is in years. Write the model in the form y = a · b^t and find the percent growth per year to the nearest tenth of a percent.

Problem 14 Model from a table ★★★

The table shows an investment’s value. Show that the growth is exponential, state the percent growth per year, and write the model.

Problem 15 Doubling an investment ★★★

An account starts with $5,000 and earns 6% compounded annually. Make a table of the balance for 10, 11, and 12 years to find the first whole year when the balance is at least $10,000.

Problem 16 A shrinking town ★★★

A town of 12,500 people loses 2.5% of its population each year. Write the model, make a table for 7, 8, and 9 years, and find the first whole year when the population is below 10,000. The figure shows the trend.

Problem 17 Carbon dating ★★★

Carbon-14 has a half-life of 5,730 years. What fraction of the original amount remains after 11,460 years, and what percent remains after 2,865 years?

Problem 18 Effective annual yield ★★★

A savings account pays 6% compounded monthly. Find the effective annual yield, which is the percent increase in one year. Compare it with the yield when the 6% is compounded continuously.

Problem 19 Choosing between two offers ★★★

Offer A: deposit $3,000 at 5% compounded quarterly for 7 years. Offer B: deposit $2,950 at 5.2% compounded continuously for 7 years. Find the value of each offer and decide which is greater.

Problem 20 Model from two data points ★★★

An exponential model y = a · b^t gives y = 330 when t = 1 and y = 399.3 when t = 3. Find a and b, and predict y when t = 5.