Question

A tank filled with water begins draining. The number of minutes t since the water began draining from the tank is a function of the number of gallons of water in the tank, v. We will call this function f so that f(t) = v.

Required:
a. Using function notation, represent the of gallons of water in me tank 4 minutes after the water darning from the Ink.
b. Suppose that f(4) = 7, what does this mean in the context of the problem?

Answer 1

`(a)\ f(4) = v`

(b) There are 7 gallons left in the tank after 4 minuted

Explanation:

Given

`f(t) = v`

`t \to` time since water began draining

`v \to` gallons in the tank

Solving (a): Notation for gallons remaining at 4 minutes

This means that
`t=4`

`f(t) = v` becomes

`f(4) = v`

Solving (b): Interpret f(4) = 7

We have:

`f(t) = v`

`t \to` time since water began draining

`v \to` gallons in the tank

This means that:

`t =4`

`v =7`

It can be interpreted as:

There are 7 gallons left in the tank after 4 minuted