The dollar value v(t) of a certain car model that is t years old is given by the following exponential function. v(t)=24,500(0.95^t) find the initial value of the car and the value after 13 years. round answers to the nearest dollar as necessary.

The dollar value v(t) of a certain car model that is t years old is given by the following exponential function. v(t) = 29,900(0.80^t) Find the initial value of the car and the value after 12 years. Round your answers to the nearest dollar as necessary

V(0)=29,900 X .80^0=29,900 X 1=$29,900 initial value of the car.

V(12)=29,900 X .80^12

V(12)=29,900 X 0.068719476736=$2,054.71value of the car after 12 years.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

i think it might be a but you might want a second opinion