Question

The value of a truck bought new for $32,000 decreases 16.5%each year. Write an exponential function, and graph the function.Use the graph to predict when the value will fall to $3000.

Answer 1

The exponential decay function can be written as :

`f(t)=P(1-r)^t`

where P = initial amount

r = rate of decay (decreasing value)

t = time in years

From the problem, we have :

P = $32,000

r = 16.5% or 0.165

The function will be :

`\begin{gathered} f(t)=32000(1-0.165)^t \\ f(t)=32000(0.835)^t \end{gathered}`

Using desmos, the graph of the function will be :

Then use the graph to predict when the value will fall to $3000

That will be :

in about 13 years, the value will fall to $3000

ANSWER :

The function is :

`f(t)=32000(0.835)^t`

The value will fall to $3000 in about 13 years.