Question

The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria increase in population is shown by the formula G= (t)/(3.3log(base a)P)
where t is the time period of the population increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the end of the time period. If the generation time for the bacteria is 4.5 hours, how long will it take 4 of these bacteria to multiply into a colony of 7,525 bacteria? Round to the nearest hour.

Answer 1

That's a complicated description of 7525 = 4*[2^(t/G)]

solve this by taking logarithms of both sides, finding t.

Answer 2

lol tell me about it! do ya mind walking me through it? i have no idea what I'm doing lol

Answer 3

@RadEn could you help please?

Answer 4

is it 95 hours?

Answer 5

don't worry about it anymore

Answer 6

When things double in each of n steps, you have the factor
2 being applied n times: so that in three doubling times, you have
A go to A*2*2*2= A*2^3 = 8 A.

I used t/G to determine how many doubling times (and this could be a decimal number,

then got 4 * 2^(t/G) = 7525

take logarithms

log 4 + (t/G) log 2 = log (7525) = 3.877

(t/G) = [3.877 - log 4]/(log 2) = (3.877 - 0.602)/(0.301)

t/G = 10.88

t = 48.96, if I haven't made any calculation mistakes

Quick check: 2^11 = 2048 and 4*2048=8192, which is close to your 7525.

Exact check: 2^10.88 = 1884.5 and that x 4 = 7538, almost exactly matched.