
Read pages 387390 Example 1 in your textbook, Principles of Mathematics 12.
Complete the Your Turn questions on page 390 (a and b) and page 392 (a and b) for practice using exponential growth to model financial scenarios.
Click here to verify your answers.


The Your Turn question on page 392 of your textbook introduced the term appreciation. Appreciation is a financial scenario that can be modelled by exponential growth. Now, consider a financial example that uses exponential decay, depreciation.


Matt bought a new car for $25 000. The car depreciates approximately 15% of its value each year. Write an exponential equation to model the decay value of this car. Use the equation to determine the value of the car in 10 years.

Work from y = ab^{x}.
This scenario relates decrease in value to time. Therefore, the value of the vehicle is the dependent variable, y, and time, t, in years is the independent variable, x.
The original value of the car, $25 000, corresponds to the initial value, a.
The vehicle depreciates 15%; so, the decay rate is 0.15. From this, you find b = 1  0.15 = 0.85.
The exponential function that models the decay value of the car is y = 25 000(0.85)^{t}.
To find the value of the car after 10 years, substitute t = 10.
y = 25 000(0.85)^{t} 

y = 25 000(0.85)^{10} 
To find the value of the car after 10 years, substitute t = 10. 
y = 4 21.86 

The value of the car after 10 years is $4 921.86.


Read pages 390392 Example 1 in your textbook, Principles of Mathematics 12.
Complete the questions on page 397 (12a, 12b, and 12c) for practice using exponential decay to model financial scenarios.
Click here to verify your answers.


Another financial application to consider is loans. Complete the following work in your textbook that explains how exponential regression relates to loan repayment.

Read pages 392393 Example 3 in your textbook, Principles of Mathematics 12.
Complete the Your Turn questions on page 393 (a, b and c) for more practice.
Click here to verify your answers.
Read page 376 In Summary, page 394 In Summary, and page 401 Frequently Asked Questions in your textbook, Principles of Mathematics 12.

