A public swimming pool that holds 45,000 gallons of water is going to be drained for maintenance at a rate of 100 gallons per minute. The amount of water w (in gallons) in the pool after t minutes is given by the function w = 45,000 - 100t. Graph the function. Identify its domain and range. How much water is in the pool after 60 minutes? How many minutes will it take to empty the pool?

Answer: for the first question, after an hour there would be 39,000 gallons left and it would take 450 minutes to drain the pool

Step-by-step explanation:

You multiple the minutes with the rate or which the gallons are being drained and subtract it by the total amount,

Ps can I get the brainliest answer

We want to get the domain and range, graph, and analyze the given function.

We have the function:

w(t) = 45,000 - 100*t.

First, we want to get the domain and range of the function.

The domain is defined as the possible values of the input, in this case, is the time.

The smallest value of the time is t = 0, and the largest is the value of t such that the pool is empty, so we need to solve:

w(t) = 0 = 45,000 - 100*t

t = 45,000/100 = 450

Then the domain is D = [0, 450]

The range is the set of the possible outputs, the output represents the amount of water in the pool, it goes from full to empty, so the range is:

R = [0, 45,000]

The graph of the function can be seen below.

How much water is in the pool after 60 minutes?

Just replace t by 60 in the equation.

w(60) = 45,000 - 100*60 = 39,000

This is 39,000 gallons of water.

How many minutes will it take to empty the pool?

We already found that it takes 450 minutes.

If you want to learn more, you can read:

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