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 $V,P \text{ and } t$ ?

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

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

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