Question

A child inflates a balloon, admires it for a while and then lets the air out at a constant rate. If V(t) gives the volume of the balloon at time t, then the figure attached inside shows V ' (t) as a function of t.

a) At what time does the child begin to inflate the balloon?
The child begins to inflate the balloon at t=_______

b) At what time does the child finish inflating the balloon?
The child finishes inflating the balloon at t=____

c) At what time does the child begin to let the air out?
The child begins to let the air out at t=____

**please explain! thanks!:)

Answer 1

figure!

Answer 2

Since when did you start calculus? Is this a course ?

Answer 3

@phi can help you :)

Answer 4

yeah i'm in calculus:)

and yeah i'm in ap calculus:)

Answer 5

lol oops just realized that that was a very redundant sentence lol

and okie @dumbcow :)

Answer 6

haha tried answering both your questions @phi and ended up saying pretty much the same thing hahaa

Answer 7

V' is "change in volume"

the ballon starts to inflate when V ' is bigger than 0

Answer 8

so the child begins to inflate the balloon at t=4?

Answer 9

yes

Answer 10

okie:)

and finished blowing up the balloon at t=5 or 6? :/ not sure if i'm at the right place :/ or looking at the right thing on the graph :/

Answer 11

When the rate of change in volume is zero, then the balloon has stopped inflating.

Answer 12

no... v' > 0 means the balloon is getting bigger. At t=4 the air goes into the balloon. The amount of air per second increases (rate goes up) until it goes in at a rate of 2 per second

Answer 13

at about t=11 the air is still going into the balloon, but at a slower rate. It finally stops going in (and the balloon stops growing) at t=12

Answer 14

ohh okay i see

so a) t=4
b) t=12

and let's see... c) the child lets the air out at t=20 ? :/

Answer 15

would those all be right? :o

Answer 16

yes

Answer 17

yay!! thank you!!:)