Question

A culture started with 4,000 bacteria. After 2 hours it grew to 4400 bacteria. Predict how many bacteria will be present after 13 hours round your answer to the nearest whole number.

Answer 1

7436

Explanation:

y = ab^x

a = 4000

b = 4400/4000 = 1.1

x = t/2

4400 = 4000e^2k

e^2k = 1.1

k = ln 1.1/2 = .0477 to 4 dp

N(13) = 4000e^(13*.0477) = 7436

Answer 2

idk why they want the dratted "k" . it is so simple w/o it !
in the form y = ab^x, a = 4000, b = 4400/4000 = 1.1, x = t/2
N = 4000*1.1^(13/2) = 7432 <------
-----------------
now you won't be satisfied with simplicity, so
4400 = 4000e^2k
e^2k = 1.1
k = ln 1.1/2 = .0477 to 4 dp
N(13) = 4000e^(13*.0477) = 7436 <------

note that apart from a roundabout way, you get a less accurate ans !