Values of the function V give the volume of a balloon at each number of seconds t while being blown...

Values of the function V give the volume of a balloon at each number of seconds t while being blown up by a clown for 15 seconds. The function rV , defined as

1
r (t) = ⎛ 3 t⎞ 3 , give the rate of change of V with respect to t in cm3/sec at each

V ⎜⎝4π ⎟⎠
moment of t, 0 ≤ t ≤ 15 seconds.

a) b)

c) d)

e) f)

At what rate is the balloon being blown up at 3.8 seconds since the clown started blowing up the balloon? Be sure to include the rate’s unit.

At 3.8 seconds since the clown began blowing up the balloon, the volume of the

balloon is 2.19386 cm3 . What , approximately, will be the volume of the balloonat 4.1 seconds?

Approximately how much will the volume of the balloon have changed between 3.8 seconds and 4.7 seconds? Use one change of 0.9 seconds.

Using your work in 1.c what, approximately, will be the volume of the balloon at 4.7 seconds? (Use the fact that at 3.8 seconds since the clown began blowing up

the balloon, the volume of the balloon is 2.19386 cm3 .)
Revise your estimate in 1.c by estimating how much the volume of the balloon

will have changed every 0.3 seconds from 3.8 to 4.7 seconds.

Using your revised estimate in 1.e, what will be the approximate volume of the balloon at 4.7 seconds? (Use the fact that at 3.8 seconds since the clown began

blowing up the balloon, the volume of the balloon is 2.19386 cm3 .)