Question

Suppose that the concentration of a bacteria sample is 60 comma 000 bacteria per milliliter. If the concentration triples in 4 ​days, how long will it take for the concentration to reach 102 comma 000 bacteria per​ milliliter?

Answer 1

1.932 days (or approximatelly 1 day, 22 hours and 22 minutes)

Explanation:

The inicial concentration is 60,000, and this concentration triples every 4 days, so we can write the equation:

P = Po * r^t

where P is the final concentration after t periods of 4 days, Po is the inicial concentration and r is the ratio that the concentration increases (r = 3)

Then, we have that:

102000 = 60000 * 3^t

3^t = 102/60 = 1.7

log(3^t) = log(1.7)

t*log(3) = log(1.7)

t = log(1.7)/log(3) = 0.483

so the number of days that will take is 4*0.483 = 1.932 days (or approximatelly 1 day, 22 hours and 22 minutes)