Question

A 50-gallon rain barrel is filled to capacity. It drains at a rate of 10 gallons per minute. Write an equation to show how much water is in the barrel after x minutes of draining. Then make a graph for this function

Answer 1

The quantity of water drain after x min is 50
`(0.9)^(x)`

Explanation:

Given as :

Total capacity of rain barrel = 50 gallon

The rate of drain = 10 gallon per minutes

Let The quantity of water drain after x min = y

Now, according to question

The quantity of water drain after x min = Initial quantity of water ×
`(1-(\textrm rate)/(100))^(\textrm time)`

I.e The quantity of water drain after x min = 50 gallon ×
`(1-(\textrm 10)/(100))^(\textrm x)`

or, The quantity of water drain after x min = 50 gallon ×
`(0.9)^(x)`

Hence the quantity of water drain after x min is 50
`(0.9)^(x)` Answer

Answer 2

`y=50-10x`

Explanation:

Let x represent number of minutes of draining.

We have been given that a barrel drains at a rate of 10 gallons per minute. So gallons drained after x minutes of draining would be
`10x`.

Since the numbers of gallons is decreasing, so slope will be negative as:

`-10x`

We are also told that the 50-gallon rain barrel is filled to capacity. This means that initial value or y-intercept is 50.

We can represent number of gallons remaining (y) after x minutes as:

`y=50-10x`

Therefore, the equation
`y=50-10x` shows the amount of water in the barrel after x minutes of draining.

Upon graphing our equation, we will get required graph as shown in the attachment.