# Rates of change - pre calc

• Mar 24th 2009, 07:03 PM
blahblahblah
Rates of change - pre calc
stone is dropped into water and ripples begin to form in a circular pattern. if the radius of the circular patter is growing at a rate of 6cm/s determine :

a) radius of the circle after ten seconds
b) the area of the circle after ten seconds
c) the instantaneous rate of change of circle area with respect to time at 10 seconds

• Mar 25th 2009, 03:28 AM
Craka
The information you have been given in the question is that for every 1s (one second) the radius of the circle get 6cm (six centimetres) bigger. That is what they mean by 6cm/s it means 6cm per second.

So for part A you just need to multiply they rate by the amount of time elapsed. $6cm/s \times 10s = 60cm$

Part B should be straight forward using result from part A.

part C does require derivatives
• Mar 25th 2009, 03:17 PM
skeeter
Quote:

Originally Posted by blahblahblah
stone is dropped into water and ripples begin to form in a circular pattern. if the radius of the circular patter is growing at a rate of 6cm/s determine :

a) radius of the circle after ten seconds
b) the area of the circle after ten seconds
c) the instantaneous rate of change of circle area with respect to time at 10 seconds

$A(t) = \pi(6t)^2$
$A'(10) = \lim_{t \to 10} \frac{A(t) - A(10)}{t - 10}$