Related Rates, i dont understand it.

[mattflint50]

Ok, heres the question from our AP review, could you help start me out. I just keep getting 15.

The radius of a sphere is increasing at a rate proportional to its radius. If the radius is 4 initially, and the radius is 10 after 2 seconds, what will the radius be after 3 seconds?

 

[Unco]

I get 15.8 (3.s.f), is that what you're getting?

Anyhow, the 'start' would be \(\displaystyle \mbox{ \frac{dr}{dt} }=\mbox{ kr}\).

 

[galactus]

The radius of a sphere is increasing at a rate proportional to its radius.

Matt:

Could that possibly be the volume is increasing proportional to the radius?.


I'm probably misinterpreting the problem, but couldn't we just use something linear since we're talking proportionality.

at+b
a(0)+b=4, b=4
a(2)+b=10
2a+4=10
a=3
r=3t+4
r=3(3)+4=13 units