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

Answer:

$A(6) = 12000 = A_o e^{-0.07 *6}$

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

$A_o = \frac{12000}{e^{-0.07*6}}= 18263.539$

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

Step-by-step 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:

$A_o = \frac{12000}{e^{-0.07*6}}= 18263.539$

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