Question

The count in a bateria culture was 500 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 minutes.

When will the population reach 13000.

Answer 1

use the model

\[A = A_{0}e^{kt}\]

so use the information to find k

\[1100 = 500e^{20k}\]

now solve for k.

for the initial population

use the 10 minute info and substitute k

\[500 = A_{0}e^{10\times k}\]

then

\[A_{0} = \frac{500}{e^{10 \times k}}\]

hope it helps

Answer 2

for the population to double just use your value of k again and solve

\[2 = e^{k \times t}\]

and solve for t

Answer 3

population after 70 mins

you need the initial population found earlier and the k value

then its

\[A = A_{0} \times e^{70 \times k}\]

Answer 4

lastly, use your k value and initial populations found earlier then

\[13000 = A_{0} \times e^{k \times t}\]

and solve for t

Answer 5

opps forgot to say

\[A = population\]

\[A_{0} = initial~~ population\]

k = growth constant

t = time in minutes