bacteria are growing continuously ina laboratory culture at an exponential rate such that the number of?

Question

bacteria triples after 2 hrs. at this rate , how many hr will the culture require to increase to five times its original size?

answer is 2.93 . pls. explain

Answer 1

well
V=V0 exp(at)
V0 - initial volume
V - volume
a - time constant
t - time

at t=2 V=3V0 then
3V0=V0 exp(2a)

so a = .5ln(3) = .549

Use the original equation for V=5V0 we have

5V0=V0 exp (.549 t)

t= ln(5)/.549=2.93hours

Answer 2

The custom grows exponentially, we can use the formula a x 2^n = b the place a is the preliminary count huge style, n is the style of time durations, and b is the count huge style after n durations. interior the question, a is unknown, n = 5, through fact 15 hours / 3 hours = 5, and b = a million,000,000 resolve the equation for a, we've a = b / 2^n Substituting our values, we get a = a million,000,000 / 2^5 = a million,000,000 / 32 a = 31,250 there have been initially 31,250 bacteria interior the custom.