Question

Determine the average rate of change over each following time interval

0 minuets to 4

Answer 1

`\text{We need to find the average rate of change over the time interval }[0,4]\\ \\ \text{we know that the average rate of change of a function f(x) over interval }[a,b]\\ \text{is given by}\\ \\ f_(avg)=(f(b)-f(a))/(b-a)\\ \\ \text{so using this concept the average rate of change over the given interval is}\\ \\ \text{average rate of change}=(A(4)-A(0))/(4-0)\\ \\ \text{from the graph, we can see that at t=0 minutes, amount of water is 40 gallons}`

`\text{and at t=4 minutes, the amount of water in the play pool is 24 gallons.}\\ \\ \text{Hence the average rate of change}=(24-40)/(4-0)\\ \\ =(-16)/(4)\\ \\ =-4`

Hence average rate of change on the given time interval is: -4