Question

A swimming pool is filled with water by a hose at a rate of 1020 gallons per hour.The amount v (in gallons) of water in the pool after t hours is given by the function v(t)=1020t. How does the graph of v change in each situation? a.A large hose is found.Then the pool is filled at a rate of 1360 gallons per hour. b. Before filling up the pool with a hose, a water truck adds 2000 gallons of water to the pool.

Answer 1

1) Original function: v(t) = 1020t

=> the graph is straight line with slope 1020 that passes through the origin (0,0)

2) Situation a. The pool is filled ad a rate of 1360 gallons per hour.

In that case, the new function is v(t) = 1360t

So, the new graphs is a straight line with a steeper slope of 1360, which also passes through the origin (0,0).

3) Situation b. Before filling up the pool with a hose a water truch adds 2000 gallons of water to the pool.

In this case, the line intercepts the y-axis at y = 2000, this is the striaght line does not pass trrough the origin but by the point (0, 2000).