A swimming 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 = t
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1 Answer

1. User Answers jacob193
Answer:
0 ≤ t ≤ 5.
Stepbystep explanation:
In the function [tex]f(t)[/tex], [tex]t[/tex] is the independent variable. The domain of [tex]f[/tex] is the set of all values of [tex]t[/tex] that this function can accept.
In this case, [tex]f(t)[/tex] is defined in a reallife context. Hence, consider the reallife constraints on the two variables. Both time and volume should be nonnegative. In other words,
 [tex]t \ge 0[/tex].
 [tex]f(t) \ge 0[/tex].
The first condition is an inequality about [tex]t[/tex], which is indeed the independent variable.
However, the second condition is about [tex]f[/tex], the dependent variable of this function. It has to be rewritten as a condition about [tex]t[/tex].
[tex]\begin{aligned} f(t) &\ge 0 &&\text{Assumption} \cr 80000  16000\, t& \ge 0 && \text{Definition of} ~ f \cr 80000 & \ge 16000\, t && \begin{aligned}&\text{Add $16000\, t$} \\[0.5em] & \text{to both sides of the inequality}\end{aligned} \cr 5 &\ge t &&\begin{aligned}&\text{Divide both sides of} \\[0.5em] & \text{the inequality by $16000$}\end{aligned} \cr t &\le 5 && \text{Flip the inequality}\end{aligned}[/tex].
Hence, t ≤ 5.
Combine the two inequalities to obtain the domain:
0 ≤ t ≤ 5.