A bacteria culture has an initial population of 25. This bacteria reproduces at a daily rate of 1.28 percent. How long will it take for the population to grow to 375 bacteria?

212.9 days

Step-by-step explanation:

The bacteria culture initial population is 25 represented by Po and the population after t days is represented by P (t).

Using growth formula:

P (t) = Po (1 + r) ^t where r is rate in percent and t is time in days

r = 1.28%, P (t) = 375, and Po = 25

substituting this values into the equation above yields

375 = 25 (1 + 1.28/100) ^t

375:25 = (1 + 0.0128) ^t

15 = (1.0128) ^t

take logarithm of both sides

log 15 = log (1.0128) ^t remember the law log a^b = b log a

applying the same law gives

log 15 = t log 1.0128

divide both side by log 1.0128

log 15 : log 1.0128 = t log 1.0128 : log 1.0128

t = 212.9 days

211 days