Question

The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 13% per year. What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?

Answer 1

Answer: 1) The value of truck initially would be $87000.

2) at t = 0 , y-axis would be cut at $67000.

Explanation:

Since we have given that

`y=A_0(0.87)^x`

Here, A₀ is the initial value.

Rate of depreciation = 13%

Number of years = x

So, The value of truck initially would be $87000.

As shown in the given figure.

If the the initial value of truck = $67000

Rate will be same but the y-intercept will change.

As change in initial value does not affect the rate but the y - intercept.

Then at t = 0 , y-axis would be cut at $67000.

Answer 2

The value of
`A_(0)` is 87000 since it is the value when t = 0

The graph would cross the y-axis at 67000 for t = 0 which is the initial value