8 pts The number of guests g in a water park t hours after 9

8 pts) The number of guests g in a water park t hours after 9 am is given by

g(t) = –32t² + 224t + 263 for 0 £ t £ 8. (t = 0 corresponds to 9 am)

Find and interpret the average rate of change of g over the interval {tl4<t<7} Show work.

g(t) = –32t^2 + 224t + 263

we have to find and interpret the average rate of change of g over the interval {t | 4 £ t £ 7} = [4, 7].

Avg rate of change = { g(7) - g(4) }/( 7-4)

g(7) = -32(7^2) +224*7 +263

= 263

g(4) = -32(4)^2 +224(4) +263

= 647

Avg rate of change = { g(7) - g(4) }/( 7-4) = ( 647 -263)/(7-4) = 128