The equation $p=13+0.625d$ approximates the pressure $p$, in pounds per square inch, exerted on a fish at a depth of $d$ feet (ft) below the surface of the water. What is the increase in depth that is necessary to increase the pressure by $1$ pound per square inch?

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It is easier to interpret these sorts of questions if we compare it to something that we're accustomed to.

We need to find the change in depth if pressure is $1$. We can use a proportion to find this value.

$$\frac{0.625\text{ pound per square inch} }{1\text{ feet} } = \frac{1 \text{ pound per square inch}}{ x \text{ feet}}$$ $$0.625x=1$$ $$x= \boxed{1.6 \text{ feet}}$$

We can test an arbitrary situation. For example, what is the change in $d$ when we change $p=0$ to $p=1$.

The difference is $-19.2-(-20.8)=\boxed{1.6 \text{ feet}}$