Answer:
212.9 days
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