8 The population of a community grows proportional to the po

8- The population of a community grows proportional to the population at time t. if the initial population P₀ doubles in 8 years,

c) how fast is the population growing when t=10 years? (show work and explanation)

Solution

P(t) is the population at time t

P\'(t) = K * P(t)

Solution

P(t) = P(0) e^(Kt)

at t = 8 , P(t) = 2P(0)

So

2 = e^(8K)

K = ln(2)/8

How fast population growing at t =10

= K*P(10)

P(10) = P(0) e^(10K) = P(0) e^(10/8 * ln(2)) = P(0) 2^(10/8)

K*P(10) = ln(2)/8 *  P(0)* 2^(10/8)

So it depends on the initial population