Question

2) A bacterial culture of population is known to have a growth rate proportional to itself. Between 6PM and 7PM, the population triples. At what time will the population become 100 times what it was at 6 P.M.

Answer 1

Answer:

10:12 PM

Explanation:

If it grew to triple it's own size from 6 PM to 7 PM, we can say the population triples every hour. Therefore:

$p = p0 * 3^t$

With t in hours.

For the population to grow 100 times

$3^t = 100$

To solve this we need to find the logarithm of base 3 of 100.

log(3)(100) = 4.2

If it started growing at 6 PM, 4.2 hours later, at 10:12 PM, it will have grown to 100 times the initial size..