Question

A scientist started with a culture of 20 bacteria in a dish. the number of bacteria at the end of each successive hour increased exponentially, so that the number at the end of one day was 220. to the nearest million, how many bacteria were there after one week?

Answer 1

Bacteria Growth Rate Formula:

N(t) = N(0) * ( 1 + r)^t

where, N(0) is the number of bacteria present at the beginning of the experiment, r is the growth rate, t is the time taken/ elapsed.

Substituting the numbers for N(t), N(0) and t from the given description, we get the value of r.

220 = 20*(1+r)^(24 hours)

Solving for r, we get r = 0.105074.

1 week has (7 x 24 = 168) hours in it.

Therefore, N(168 hours) = 20*(1+0.105074)^168

Which is approximately 390 millions.

Hence there will be 390 millions bacteria at the end of 1 week.