Question

The count in a bateria culture was 300 after 10 minutes and 1100 after 30 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?

Find the doubling period.

Find the population after 70 min.

When will the population reach 14000

Answer 1

do you have a basic model..?

Answer 2

y=a*b^t

Answer 3

is b actually e or some other number...?

Answer 4

b is the base

Answer 5

ok... so it looks like the 1st task is to find b

you know

\[300 = a \times b^{10}\]

so

\[\frac{300}{a} = b^{10}\]

equation 1

now for the other information

\[1100 = a \times b^{30}\]

or

\[\frac{1100}{a} = b^{30}\]

using some index laws you can say

\[\frac{1100}{a} = b^{10} \times b^{20}\]

substitute equation 1

\[\frac{1100}{a} = \frac{300}{a} \times b^{20}\]

so

\[b = \sqrt[20]{\frac{1100}{300}}\]

from there you should be able to get the rest of the information.

Answer 6

thanks but i really need help finding all the answers..

Answer 7

well you can't find the answer of you don't know the base...

so if you know b

then using your model you can find the initial population...

\[P = a \times b^t~~~~then~~~~ 300 = a \times b^10~~~~~so~~~~a = \frac{300}{b^{10}}\]

Answer 8

@rjin2 any feedback..?