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

 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 <------ 
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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 !

Answer 2

Answer:

7436

Step-by-step 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