Question

The equation V=23400(0.93)t represents the value (in dollars) of a car t years after its purchase. Use this equation to complete the statements below.

Answer 1

The value of this car is decreasing at a rate of 7%

The purchase price of the car is $23,400

Step-by-step explanation:

The general equation of a value of a commodity over some time period can be shown as follows:

`V=I(1+r)^t`

where :

V is the value at a certain year t

I is the initial or purchase value

r is the rate of increase or decrease

t is the time in years

It should be understood that if 1 + r is less than 1, then the value is decreasing over the years

Let us get the rate:

`\begin{gathered} 1\text{ + r = 0.93} \\ r\text{ = 0.93-1 = -0.07} \end{gathered}`

r is negative and that means there is a decrease at a rate of 7% (7% as a fraction is 7/100) yearly

Now, let us answer the questions

The value of this car is decreasing at a rate of 7%

The purchase price of the car is $23,400