The value v of a certain automobile that is t years old can be modeled by upper v left parenthesis t right parenthesis equals 14 comma 683 left parenthesis 0.78 right parenthesis superscript tv(t)=14,683(0.78)t. according to the model, when will the car be worth (a) $90009000? (b) $30003000? (c) $20002000?

The given equation is as:

We will use this equation in all the three cases to find the in years.

Case (a)

Since

Our equation will become

Dividing 14683 on both sides and taking log to the base 10 on both sides, we will get:

Thus, year

Case (b)

Since

Our equation will become

Dividing 14683 on both sides and taking log to the base 10 on both sides, we will get:

Thus, years

Case (C)

Since

Our equation will become

Dividing 14683 on both sides and taking log to the base 10 on both sides, we will get:

Thus, years

the answer is a

step-by-step explanation: