Determine if the value of the car can be modeled by an exponential growth function or not.
Error: The decay factor should be 0.86 Correction: About $11 761
Practice makes perfect
In the diagram, the value of a car in 2015 is calculated incorrectly.
To describe the error, we will first write a function modeling the value v(t) of the car after t year and then substitute 5 for t. We know that the value of a car decreases by 14 % annually, so we will use an exponential decay function. Therefore, the function v(t) is of the following form.
v(t)= a(1- r)^t
Here, a is the initial value and r is the rate of decay. In the question, the rate of decay is given as 14 %, or 0.14. The initial value of the car is 25 000. Then, the function becomes as follows.
v(t)= 25 000(1- 0.14)^t
⇓
v(t)=25 000( 0.86)^t
We see that the decay factor is equal to 0.86, not 1.14, as is written in the given solution.
Correct: & v(t)=25 000( 0.86)^t ✓
Incorrect: & v(t)=25 000( 1.14)^t *
To find the value of the car in 2015, we will substitute 5 for t.
