Abacteria 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

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