Use the difference quotient of A(r)= 1tr2 to calculate the average rate of change during certain intervals. The difference quotient of A(r) is:
T(r+h) - Trở TP + 23h + )- Tr Ter2 + 2 trh + Tth? - Tir?
= 2 tr + Tth
h
h
h
The average rate of change from the interval 2 to 3 inches is
The average rate of change from the interval 2 to 2.5 is
ve square inches per inch,
square inches per inch.

Ahigh-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. suppose that the radius r increases at the rate of 0.02 inches per second, and that r = 36 inches at time t = 0. determine the equation that models the volume v of the balloon at time t, and find the volume when t = 360 seconds. v(t) = 4π(0.02t)2; 651.44 in3 v(t) = 4π(36 + 0.02t)2; 1,694,397.14 in3 v(t) = four pi times the product of zero point zero two and t to the third power divided by three.; 4,690.37 in3 v(t) = four pi times the quantity of thirty six plus zero point zero two t to the third power divided by three.; 337,706.83 in3