Question

Dr. shepherd is studying a bacterial colony with a population of 29,600 bacteria. the colony is

growing 5% per hour. how many bacteria will the colony contain in 12 hours?
if necessary, round your answer to the nearest whole number
bacteria

Answer 1

53,157

Explanation:

The population growth of a bacterial colony can be modeled by an exponential function of the form ...

p(t) = a·b^t

where a is the initial population and b is the growth factor. The growth factor is ...

b = 1 +r

where r is the growth rate.

__

In this problem we have ...

a = 29,600

b = 1 +5% = 1.05

t = 12

So, the population after 12 hours is

p(12) = 29600×1.05^12 ≈ 53,157

The colony will contain 53,157 bacteria in 12 hours.