Question

The value of an antique car is modeled by the function

Answer 1

`V(t)=150\cdot(1.004)^t`

when we are modeling increments using functions the standard form should be

`V(t)=A\cdot(1+r)^t`

In which A represents the initial value and r represents the rate it is increasing per year.

In this case to find what is the increment per year we equal what is inside the parentheses

`\begin{gathered} 1+r=1.004 \\ r=1-1.004 \\ r=0.004 \end{gathered}`

now this decimal can be represented as a percentage if we multiply by 100

`\begin{gathered} \text{\%r}=0.004\cdot100 \\ \text{\%r=0.4\%} \end{gathered}`

It is increasing by 0.4% per year.