A bacteria culture starts with 720 bacteria and grows at a rate proportional to its size. After 6 hours there will be 4320 bacteria.

Question

A bacteria culture starts 720 with  bacteria and grows at a rate proportional to its size. After 6 hours there will be 4320  bacteria.

a) Express the population after t hours as a function of t population:

my response: 720e^(0.299t), which is correct

b)What will population be in 9 hours?

my response: 10617.42, which is incorrect and I cannot solve

c) How long will it take for the population to reach 2630?

I am unsure of my answer for this question but I got 4.33

Can someone please help with B and C

Answer 1

4320 = 720e^6k

6 = e^6k

ln 6 = 6k

1.791 ≈ 6k

0.2986 ≈ k

A ≈ 720e^(9)(0.2986)

A ≈ 720e^2.6874

A ≈ 720(14.6934)

A ≈ 10579

2630 = 720e^0.2896t

3.6528 ≈ e^0.2896t

ln 3.6528 ≈ 0.2986t

1.2955 ≈ 0.2986t

4.339 ≈ t