Question

ASAP due really soon

Answer 1

A bacteria culture starts with 500 bacteria and doubles in size every half hour.1

(a) How many bacteria are there after 3 hours?

We are told “. . . doubles in size every half hour.” Let’s make a table of the time and population:

t 0 0.5 1.0 1.5 2.0 2.5 3.0

bacteria 500 1000 2000 4000 8000 16000 32000

Thus, after three hours, the population of bacteria is 32,000.

(b) How many bacteria are there after t hours?

In t hours, there are 2t doubling periods. (For example, after 4 hours, the population has doubled 8

times.) The initial value is 500, so the population P at time t is given by

P(t) = 500 · 2

2t