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

Answer:

$y=50-10x$

Step-by-step 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.

Answer 2

Answer:

The quantity of water drain after x min is 50 $(0.9)^{x}$  

Step-by-step 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 ×  $(1-\dfrac{\textrm rate}{100})^{\textrm time}$

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

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