Question

Use this piecewise function that gives the rate, r(t), in gallons per hour, at which a pool is being filled with water at

time t hours. The pool is initially empty.
r(t) =
2501, 0 St<2
500, 2 st s 10
Based on this rate function, how many gallons of water are in the pool after 10 hours?
2,500
O 3,500
O 4,500
O 5,500

Answer 1

4500

Step-by-step explanation:

Answer 2

The correct answer is "4500".

Step-by-step explanation:

As per the question,

Total galloons of water will be:

=
`\int_(0)^(2)250 t \ dt+\int_(2)^(10)500 \ dt`

=
`250((t^2)/(2) )^2_0+500(t)^(10)_2`

=
`125(4-0)+500(8-2)`

=
`125(4)+500(6)`

=
`500+4000`

=
`4500`

Thus the above is the appropriate option.