Question

A certain population of bacteria has an average growth rate of 0.06 bacteria per hour. The formula for the growth of the bacteria's population is ࡭ = ࢕ࡼ (૛. ૠ૚ૡ) where, ࢚૟૙.૙ Po is the original population, t is time in hours, and A is the new population . If the current population of a culture was 3000 bacteria (A) and it started growing 30 hours ago, what was the original size of the bacteria (Po)?

Answer 1

522 bacteria

Explanation:

The formula given as growth rate =

A = Po (1 + r)^t

Where:

Po is the original population

t is time in hours = 30

A is the new population = 3000

r is growth rate = 0.06

3000 = Po × ( 1 + 0.06)^30

3000 = Po × 1.06^30

Divide both sides by 1.06^30

Po = 3000/1.06^30

Po = 522.33039273 bacteria

Approximately = 522 bacteria

The original size of the bacteria was 522 bacteria