Question

Suppose a spherical balloon grows in such a way that after t seconds, its volume is V = 4 sqrt(t) cm3

I found that v=52
but i cant find

How fast is the volume changing after 169 seconds?

Answer 1

i know its the derv

Answer 2

first derivative of V

Answer 3

V=4t^(1/2)
V'=4(1/2)t^(-1/2)=2t^(-1/2)

Answer 4

\[V'=\frac{2}{\sqrt{t}}\]

Answer 5

how do i solve that?

Answer 6

\[V'(169)=\frac{2}{\sqrt{169}}=\frac{2}{13}\]

Answer 7

ok thanx

Answer 8

you don't plug in 169 until you find the derivative

Answer 9

wait so i do 2/sqrt (t) then plug in 169 for t?

Answer 10

do= deriv

Answer 11

V'(t)=2/sqrt(t) <= plug in 169 now

Answer 12

ok