1. The population of bacteria in an experiment grows at a rate proportional to t

Question

1. The population of bacteria in an experiment grows at a rate proportional to the number of bacteria present at time t. After 7 hours it is observed that 5,400 bacteria are present and after 14 hours 9,600 are present.

(a) Find the growth function of the population of the bacteria and round the growth rate to the 4th decimal place.

(b) Determine the initial amount of the bacteria at the beginning of the experiment.

(c) How long it takes for the number of the bacteria to reach 100,000?

P.S. I know this is 3 questions but that is why I'm giving so many points. Thank you!

Explanation / Answer

p(t) = po e^(kt)

p(7) =5400

p(14) =9600

p0 e^(7k) = 5400

po e^(14k) = 9600

e^(7k) =9600/5400

hence po= 9600 (b)

and e^(7k) =9600/5400

7k =ln (9600.500)

k= 1.31

hence growth function is p(t) = 9600 e^(1.31t)

when p(t) = 100,000

e^(1.31t) =100000/9600

1.31t = ln ( 100000/9600)

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