Question

A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula P t = P o ⁢ 2 t d , where P o is the original number of bacteria cells, P t is the number after t hours, and d is the time taken to double the number.

Answer 1

Step-by-step explanation:

Step-by-step explanation:

I would write the growth function as:

y

=

100

e

k

t

So that at

t

=

0

we get:

y

=

100

e

0.02

⋅

0

=

100

bacteria.

At

t

=

5

hours we will get:

y

=

100

e

5

⋅

0.02

=

110

bacteria.

To double the initial number we need to solve:

200

=

100

e

0.02

t

e

0.02

t

=

2

Apply natural logs to both sides:

ln

(

e

0.02

t

)

=

ln

(

2

)

0.02

t

=

ln

(

2

)

t

=

ln

(

2

)

0.02

=

34.65

≈

34.6

34

hours and 36 minutes approx.