Question

A graphing calculator is recommended. A bacteria culture starts with 300 bacteria and doubles in size every half hour. (a) How many bacteria are there after 2 hours? bacteria (b) How many bacteria are there after t hours? y = bacteria (c) How many bacteria are there after 40 minutes? (Round your answer to the nearest whole number.)

Answer 1

a) 4800 bacteria

b)
`y(t) = 300(4)^t`

c) 754 bacteria

Explanation:

A bacteria culture starts with 300 bacteria and doubles in size every half hour.

This means that the number of bacteria after t periods of half hour is given by:

`y(t) = 300*(2)^(t)`

(a) How many bacteria are there after 2 hours?

2 hours is 2*60/30 = 4 periods of 2 hours, so this is y(4).

`y(4) = 300*(2)^(4) = 300*16 = 4800`

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

It doubles every half hour, so each hour, it is multiplied by 4. Then

`y(t) = 300(4)^t`

(c) How many bacteria are there after 40 minutes?

40 minutes is 40/30 = 1.33 periods of half hour. So this is y(1.33).

`y(1.33) = 300*(2)^(1.33) = 754`