Problem 7 Algebra help needed

Question

The large watering tank on a ranch holds 500 gallons of water when it is full, at time x=0, The tank is full but an angry stallion has kicked a hole in it. The water begins leaking out at a constant rate of 16 gallons per minute. Let f(x) be the number of gallons in the tank after x minutes.

A) Write the equation of a linear model using function notation ____

B)Find and interpret f(15).

C)Find the x intercept by finding x when f (x)=0. Interpret its meaning in this situation.

Answer 1

Hi Angeles L

The slope intercept form can be used to represent your situation

y = mx + b

y = f(x) = mx + b

m = rate of loss 16 for 16 gallons per minute, it is a loss so the sign will be negative

Equation is f(x)= -16x + 500

f(15) = -16(15) + 500 = 260

When f(x) = 0 then x is 500/16

x intercept is 31.25 minutes

The function represents a continuous loss of water from a full tank (500 gals=full tank) at a rate of 16 gallons per minute. When x is zero this represents when the tank was full before the horse kicked a hole in it. When f(x) is zero this gives the time it took to empty the 500 gallon tank.

I hope this helps