Question

A culture of bacteria doubles every 2 hours.

a. Explain how this situation can be modeled with a sequence.
b. If there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours?

Answer 1

2,048,000.

Explanation:

a. Let the initial number of bacteria = x

Since bacteria doubles every 2 hours, so the sequence will be in the form of

x, 2x, 4x, 8x, .........

This sequence is a geometric sequence with a common ratio of 2.

b. Since explicit formula for a geometric sequence is

`P_(n) =P_(0)(r)^(n)`

Where,
`P_(n)` = population of bacteria after n hours.

`P_(0)` = Initial population

r = common ratio

n = number of times population got doubled

By putting the values of each term in the formula :

`P_(24) =500(2)^(12)`

=
`500* 4096`

= 2,048,000

After 24 hours population of bacteria would be 2,048,000.