contestada

Suppose that the dollar value v(t) of a certain car that is t years old is given by the following exponential function.v (t) = 19,900(0.91)^tFind the initial value of the car.Does the function represent growth or decay?By what percent does the value of the car change each year?

Respuesta :

The general form of an exponential function is:

[tex]f(x)=ab^x[/tex]

where a = initial value and b = the rate of growth.

In the given equation that we have,

[tex]v(t)=19,900(0.91)^t[/tex]

we can see that the value of a = 19, 900. Hence, this is the initial value of the function and thus, the initial value of the car is 19, 900.

We can also see that the rate of growth is 0.91. Since the rate of growth is between 0 and 1, the function represents exponential decay.

The value of the car decreases by 9% each year.