A colony of bacteria grows exponentially. The colony begins with 3 bacteria, but 2 hours after the beginning of the experiment, it has grown to 50 bacteria. (a) Give a formula for the number of bacteria, P, as a function of time t in hours. Round your answer for the hourly growth rate to four decimal places. P=    (b) How long does it take for the colony to triple in size? Round your answer to two decimal places. The colony triples in size in.              hour(s).

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Asked Oct 25, 2019
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A colony of bacteria grows exponentially. The colony begins with 3 bacteria, but 2 hours after the beginning of the experiment, it has grown to 50 bacteria.

 

(a) Give a formula for the number of bacteria, P, as a function of time t in hours.

 

Round your answer for the hourly growth rate to four decimal places.

 

P=    

 

(b) How long does it take for the colony to triple in size?

 

Round your answer to two decimal places.

 

The colony triples in size in.              hour(s).
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Expert Answer

Step 1

The exponential function is as follows.

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P Pe where P is the population after time ""| P, is the initial population e is a constant t time taken

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Step 2

Obtain the k value as follows.

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50 3e2 50 >e2* 50 2k In 3 50 In 3 1.4 2 k =

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Step 3

(a) Obtain the formula for the number of bacteria, P, a...

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1.4 P = P = 3e14r

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