Question

Suppose that the dollar value y (t) of a certain house that is t years old is given by the following exponential function.

Answer 1

EXPLANATION :

Note that the Exponential growth or decay function is :

`y=A(1+r)^t`

where y = final value

A = initial value

(1 + r) = growth or decay factor

r = rate of growth or decay

t = time in years

The function is growth if the expression (1 + r) is greater than 1 and it is decay if (1 + r) is less than 1.

From the problem, we have :

`v(t)=344500(0.81)^t`

where v(t) is the final value.

The initial value of the house is $344500

Since the value of the parenthesis is 0.81 which is less than 1, the function is decay

Let's solve the rate of decay (r) :

`\begin{gathered} 1+r=0.81 \\ r=0.81-1 \\ r=-0.19 \end{gathered}`

This will be the rate of change each year.

The rate of change is -19% each year.