Question

13. A population of 50 bacteria in a laboratory culture

doubles every 30 min. The function p(x) = 50 • 2^x

models the population, where x is the number of

30-min periods.


a. How many bacteria will there be after 2 h?


b. How many bacteria will there be after 1 day?

Answer 1

Answer:

A. 800 bacteria

B. 1.41 * 10^16 bacteria

Step-by-step explanation:

The model we have is

p(x) = 50 • 2^x

Doubling time is 30 minutes each

a. For 2 hours, we shall need to calculate the number of 30-minutes in 2 hours. That is 4

Thus the population after 2 hours would be

P(x) = 50 * 2^(4) = 50 * 16 = 800 bacteria

B. After one day

The number of hours in a day is 24;

since 60 minutes makes one day, the number of 30 minutes in a day would be 60/30 * 24 = 48

There are 48 30-minutes in a day

Thus the population of the bacteria after one day will be

P(x) = 50 * 2^48 = 1.41 * 10^16 bacteria