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### Course: Algebra (all content)>Unit 7

Lesson 18: Modeling situations by combining and composing functions (Algebra 2 level)

# Model with function combination

## Problem

A partially filled pool has $10,000$ liters of water in it when Finn begins to fill it with a hose on a hot, sunny day. The volume, $V$, in liters, of water coming out of the hose in $m$ minutes is given by the function $V\left(m\right)=20m$, and the volume, $E$, in liters, of water evaporating in $m$ minutes is given by the function $E\left(m\right)=0.1m$.
Let $P$ be the total volume, in liters, of the water in the pool $m$ minutes since Finn started filling it.
Write a formula for $P\left(m\right)$ in terms of $V\left(m\right)$ and $E\left(m\right)$.
$P\left(m\right)=$
Write a formula for $P\left(m\right)$ in terms of $m$.
$P\left(m\right)=$