Question

The population (P) of a town increases with time (t) according to P(t) = Aekt where A and k are constants.

Given that at t = 0 P = 1000 and P = 3000 when t = 5, find k.
(Give your answer to 2dp)

Answer 1

To find the value of k in the exponential growth equation Aekt, solve the two equations P(0) = A and P(5) = Aekt for k using the given population values.

Step-by-step explanation:

To find the value of k in the equation P(t) = Aekt, we can use the given information to set up two equations:

When t = 0, P = 1000:

1000 = Ae^k(0) = A

When t = 5, P = 3000:

3000 = Ae^k(5)

Solving these equations:

3000 = 1000e^5k

e^5k = 3

Take the natural logarithm (ln) of both sides:

5k = ln(3)

k = ln(3) / 5

To 2 decimal places, k ≈ 0.22