growth rate question

Question

A bacteria culture starts with 3000 bacteria and grows to a population of 11 000 after 3 hours.

If the growth rate remains unchanged, how long will the population take to reach 1.68 million? Express the answer in hours : minutes : seconds.

Answer 1

11000 = 3000e^3k

3.666 ≈ e^3k

ln 3.666 ≈ 3k

1.299 ≈ 3k

0.433 ≈ k

1.69 x 10⁶ = (3.0 x 10³)e^0.433t

5.633 x 10³ = e^0.433t

ln 5.633 + ln 1000 = 0.433t

1.729 + 6.908 ≈ 0.433t

8.637 ≈ 0.433t

19.946 ≈ t