word problem

Question

The number of bacteria N­ at a certain time t is given by N = 100e^t /10, when there are 100 bacteria at time t = 0 hours. Find how many hours t it takes for the bacteria to double (that is, increase from 100 to 200 bacteria). [Use either ln(2) ≈ 0.7 to approximate your answer as appropriate.]

Answer 1

N(t) = 100 e^t/10

 

Set N(t) = 2N(0) = 200 and solve for t.

 

200 = 100 e^t/10

 

2 = e^t/10

 

t/10 = ln2

 

t = 10 ln2 ≅ 6.93 hours