Chapter 7.7, Problem 29PPS

(a)

To determine

To Find: To represent the given information in an exponential function.

.

Answer to Problem 29PPS

The equation is $w(t)=20500e^{-0.005t}$

Explanation of Solution

Given information: Maximum volume, Current volume and evaporation rate.

Given that

  $\begin{array}{l}\text{maximum}\text{volume}=20,500\text{gallons,}\\ \text{current}\text{volume}=19,000\text{gallons}\text{and}\\ \text{evaporation}\text{rate}=0.5\%\text{per}\text{hour}.\end{array}$

Thus, the required equation is

  $w(t)=20500e^{-0.005t}$

(b)

To determine

To Find: To write a function which express the amount of water pumped into the pool.

Answer to Problem 29PPS

Required equation is $p(t)=300t$ .

Explanation of Solution

Given information: The pool is refill at the rate of 300 gallons per hour.

Since, the pool is refill with 300 gallons per hour.

So, at t hours the pool is refilled by

  $p(t)=300t$

(c)

To determine

To Find: To write a function which express the sum of $w(t)+p(t)$ .

Answer to Problem 29PPS

Required equation is $p(t)=300t$ .

Explanation of Solution

Given information: Equations of $w(t)$ and $p(t)$

The required equation is

  $\begin{array}{l}C(t)=w(t)+p(t)\\ C(t)=20500e^{-0.005t}+300t\end{array}$

The function C(t) represent the net increase of water in the pool.

(d)

To determine

To Graph: To write a function which express the amount of water pumped into the pool.

Answer to Problem 29PPS

Required answer when $t=0$ .

Explanation of Solution

Given information: The function $C(t)=20500e^{-0.005t}+300t$

Graph:

  

Interpretation: From the graph initially the pool is full when $t=0$ as t increases the water flows from the pool as maximum capacity of the pool is 20,500 gallons