Question

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 minutes is given by the function V(m)= 20m, and the volume, E, in liters, of water evaporating in minutes is given by the function E(m)= 0.1m. Let P be the total volume, in liters, of the water in the pool minutes since Finn started filling it.

A. Write a formula for P(m) in terms of V(m) and E(m).
B. Write a formula for P(m) in terms of m.

Answer 1

A. P(m)=10000+V(m)-E(m)

B. P(m)=P(m)=10000+19.9m

Explanation:

Answer 2

(a)Total volume, P(m) = 10000 + V(m) - E(m)

(b)P(m)=10000+19.9m

Explanation:

The partially filled pool has 10,000 liters of water in it.

The pool is being filled with a hose, which means it adds to the volume of water. Therefore, V(m) is an addition to the total volume.

Water evaporates from the pool, which is a reduction to the volume of water. Therefore, E(m) is a subtraction from the total volume.

Therefore:

The Volume of Water in the Pool at any time, P(m) = 10000 + V(m) - E(m)

(b) Since we are given:

V(m)=20m

E(m)=0.1m

P=10000+20m-0.1m

The Total Volume, P(m)=10000+19.9m