Question

Ninas car exponentially depreciates at a rate of 7 percent per year. If nina bought the car when it was 6 years old for 12000, what was the original price of the car

Answer 1

the original price of the car would be $17,040 brand new
hope this helps

Answer 2

`A(6) = 12000 = A_o e^(-0.07 *6)`

And solving for the initial amount
`A_o` we got:

`A_o = (12000)/(e^(-0.07*6))= 18263.539`

So then the original price for the car would be approximately 18263.539$

Explanation:

For this case we can use the exponential model given by:

`A(t) = A_o e^(bt)`

Where:

`A_o` represent the initial amount for the car

`b=-0.07` represent the exponential growth/decay rate

t represent the number of years. With t =0 at the begin

After 6 year we have that t =6, and we know this condition:

`A(6) = 12000`

So then we can use the exponential model formula and the condition given and we have this:

`A(6) = 12000 = A_o e^(-0.07 *6)`

And solving for the initial amount
`A_o` we got:

`A_o = (12000)/(e^(-0.07*6))= 18263.539`

So then the original price for the car would be approximately 18263.539$