Question

In a lab experiment, 60 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 21 hours. How long would it be, to the nearest tenth of an hour, until there are 107 bacteria present?

Answer 1

What your looking for is an exponential growth or population growth formula, which is:

$T=P*(n^x)$

• T is the final population (107)
• P is the initial (starting) population (60)
• n is the multiplying factor (2/doubling)
• x is the time/period (21)

For this specific question you're trying to solve 'x' for this equation:

$107=60*(2^{\frac{x}{21}})$

(x/21 has been used as this formula usually deals with 1 hour/day/etc periods not 21 or other numbers)

If you put that formula into a calc to solve for x (e.g. symbolab) then you get the time for the population growth (right side) to equal the desired population amount (left)

Therefore, the time it take the bacteria to reach 107 is 17.526hrs