A21,000 gallon swimming pool contains 9000 gallons of water when a hose is placed into the pool and begins adding water at a rate of 1500 gallons per hour. use the segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed into the pool until it is full.

Step-by-step explanation:

We know that:

So, the pools needs 12,000 gallons more to be full. So, to solve the problem we could apply the rule of three. If 1500 gallons takes 1 hour, how much time would take 12,000 gallons:

So, using a linear model, it would take 8 hours to reach the maximum capacity of the swimming pool.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.