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

Respuesta :

Answer:

The correct answer is "4500".

Explanation:

As per the question,

Total galloons of water will be:

=  [tex]\int_{0}^{2}250 t \ dt+\int_{2}^{10}500 \ dt[/tex]

=  [tex]250(\frac{t^2}{2} )^2_0+500(t)^{10}_2[/tex]

=  [tex]125(4-0)+500(8-2)[/tex]

=  [tex]125(4)+500(6)[/tex]

=  [tex]500+4000[/tex]

=  [tex]4500[/tex]

Thus the above is the appropriate option.

Answer:

4500

Explanation: