Question

A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 7 cm per second. Write a formula to expresses the radius of the circle, r (in cm), in terms of the number of seconds, t , since the circle started growing.

Answer 1

r = 7t

or not mathematically,

r(t) = 7t

r(t) means, r, which is a function of t.

Explanation:

Initial size of the radius = 0 cm, at t = 0 s

Rate of increase of the radius of the circle = 7 cm/s

dr/dt = 7

dr = 7 dt

∫ dr = 7 ∫ dt

r = 7t + C (C is the constant of integration)

At t = 0, r = 0,

0 = 0 + C

C = 0

r = 7t.

r(t) = 7t