Chapter 4.2, Problem 42PPS

To determine

To find: The best equation of line from

  $\begin{array}{l}A\mathrm{...}y=-\frac{1}{3}x+72\\ B\mathrm{...}y=2x+225\\ C\mathrm{...}y=8x+4\end{array}$

That represents best the situation that

The current water level of a swimming pool in Tucson ,Arizona , is 6 feet.The rate of evaporation is $\frac{1}{3}$ inch per day.

Answer to Problem 42PPS

The equation $y=-\frac{1}{3}x+72$ best represents the given situation.

Where

x = number of days

y = water level in the swimming pool after x days (in inches)

Explanation of Solution

Given information: The current water level of a swimming pool in Tucson ,Arizona , is 6 feet.The rate of evaporation is $\frac{1}{3}$ inch per day.

Formula Used: 1 feet = 12 inches

Calculation:

We need to form and equation for the given situation.

Let x represent the number of days

y represent the water level in the swimming pool after x days (in inches)

Since , rate of evaporation is $\frac{1}{3}$ inch per day.

We have , evaporated water from swimming pool after x days = $\frac{1}{3}x$

Since, the swimming pool had initial water level of 6 feet.

Since, 1 feet = 12 inches

So, 6 feet = 12(6) inches

So, 6 feet = 72 inches

We have , water left in the pool after evaporation of $\frac{1}{3}x$ water from pool after x days (y) = $72-\frac{1}{3}x$ inches.

So, the best suited equation for the water level left in the pool after x days of evaporation (y) is given by :

  $y=-\frac{1}{3}x+72$