The value of phone depreciates over \(t\) years according to the formula below, where \(P\) is the original price and \(r\) is the annual rate of depreciation.

$$ V=P(1-r)^t $$

Which of the following expresses \(r\) in terms of \(V,P \text{ and } t\) ?

Summary Submit

$$ V=P(1-r)^t $$ $$ \frac{V}{P}=(1-r)^t $$

We can raise both sides to the \(\dfrac{1}{t}\) value, in order to cancel out the exponent on the right side. \(x^{\frac{1}{t}}=\sqrt[t]{x} \)

$$ \sqrt[t]{\frac{V}{P}}=1-r $$ $$ \boxed{r=1-\sqrt[t]{\frac{V}{P}}} $$