500 gallon tank is initially full of water and being drained at a rate of 10 gallons per minute

Question

(a) Write a formula for a linear function W that gives the number of gallons of water in the tank after t minutes.

​W(t)=enter your response here

​(Type an expression using t as the variable. Do not​ factor.)

Part 2

​(b) How much water is in the tank after

2

​minutes?

After

2

​minutes, the tank contains

enter your response here

gallons water.

Part 3

​(c) Graph function W and identify and interpret the intercepts. Choose the correct graph below.

the t-intercept is

interpret the t-intercept

the w-intercept is

interpret the w-intercept

d) Find the domain of W. Choose the correct domain of W below.

Answer 1

It's linear, so y = mx + b or in this case W(t) = mt + b

The slope (m) = 10 gal/min. b = the W-int = 500 (when t = 0)

W(t) = -10t + 500

All the answers to the various questions can be answered with that equation (see Max P.'s response).

Answer 2

W(t) = initial amount - rate of change * time

Plugging in the numbers from the problem

W(t) = 500 - 10*t

W(2) = 500 - 10*2 = 480 gallons

t-intercept is when W=0

0 = 500-10*t

10t = 500

t=50

W intercept is when t=0

W = 500 - 10*0 =500

Since the equation is linear use the points (50,0), (0, 500) and draw a line between them

there can't be negative water or negative time

So t >= 0

and since the W intercept is at t=50

t <= 50

As any time after that would lead to negative water

so the domain it 0 <= t <= 50