Question

Elise is buying a new car selling for $21,450. The rate of depreciation on this type

of car is 8% per year.
y=a*b^t
(1) What is the decay factor for the exponential equation?
(2) What is the initial value for the exponential equation?
(3) How would you write the equation for this situation?
(do not use x for time, but use * for times)
(4) What is the domain of the exponential function?
(5) What is the range of the exponential function?

Answer 1

The decay factor, initial value, equation, domain, and range of an exponential equation representing car depreciation are explained.

Step-by-step explanation:

To solve this problem, we can use the formula for exponential decay: y = a * b^t. Here's how we can answer each part of the question:

1. The decay factor, b, is equal to 1 minus the rate of depreciation as a decimal. In this case, the rate is 8%, so the decay factor is 1 - 0.08 = 0.92.
2. The initial value, a, is the starting price of the car. In this case, it is $21,450.
3. The equation for this situation is y = 21450 * 0.92^t, where t represents the number of years.
4. The domain of the exponential function is all real numbers, or (-∞, ∞).
5. The range of the exponential function is all positive real numbers, or (0, ∞).