Robert J. answered • 06/28/13

Certified High School AP Calculus and Physics Teacher

It should be dp/dt = rp.

Separating variables,

dp/p = rdt

lnp = rt + c

p = Ce^(rt)

a) 2C = Ce^(r*30)

r = ln(2) /30

b) 2C = Ce^(r*N)

r = ln(2) /N

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Attn: There is a quick way to get the answer for any exponential growth or decay.

C = C_{0} (2)^(r*t)

2C_{0} = C_{0} (2)^(r*N)

Solve for r,

r = ln(2)/N