Word problems requiring logarithims

Question

A certain type of bacteria, given a favorable growth medium, doubles in population every day. If you begin with 10 bacteria, how many days will it take for the population to reach 20,000?

Answer 1

Measure t in days.

r, the rate of growth is ln 2 = 0.69314718

 

solve for t

 

20000 = (10) e^(0.69314718 t)

 

2000 = e^(0.69314718 t)

 

ln2000 = 0.69314718 t

 

7.60090246/0.69314718 = t

 

10.96578428 = t

 

the 11th day, but you start on day 1, so:  11 - 1 = 10

 

10 days elapsed time