Question

Suppose that the dollar value v(t) of a certain house that is t years old is given by the following exponential function.v (t) = 325.900(0.92)Find the initial value of the house.Does the function represent growth or decay?growth decayBy what percent does the value of the house change each year??

Answer 1

Given the exponential function:

`v(t)=325,900(0.92)^t`

to find the initial value of the house, we can make t = 0 and evaluate on v(t):

`\begin{gathered} t=0 \\ \Rightarrow v(0)=325,900(0.92)^0=325,900 \end{gathered}`

then, the initial value of the house is $325900

Notice that the rate factor on the function is 0.92, which, since it is less than 1, shows a decay rate.

Finally, since the decay factor is 0.92, we have that the house each year losses 100-92=8% of its value