Aswimming pool is being drained so it can be cleaned. the amount of water in the pool is changing according to the función f(t)= 80,000 - 16,000t , where t = time in hours and f(t) = amount of water in liters. what is the domain of this function in this situation? explain how you found your answer.

0 ≤ t ≤ 5.

Step-by-step explanation:

In the function , is the independent variable. The domain of is the set of all values of that this function can accept.

In this case, is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words,

The first condition is an inequality about , which is indeed the independent variable.

However, the second condition is about , the dependent variable of this function. It has to be rewritten as a condition about .

.

Hence, t ≤ 5.

Combine the two inequalities to obtain the domain:

0 ≤ t ≤ 5.

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: