Question

The count in a bacteria culture was 700 after 10 minutes and 1500 after 35 minutes. Assuming the count grows exponentially, what was the initial size of the culture? / Find the doubling period. / find the population after 80 minutes. / When will the population reach 14000?

Answer 1

The size of the culture as a function of time can be expressed as:
\[\large y=Ae^{kt}\ .........(1)\]
where A is the initial size and k is the growth constant.
Plugging the given values into equation (1) gives:
\[\large 700=Ae^{10k}\ ...........(2)\]
and
\[\large 1500=Ae^{35k}\ .........(3)\]
Dividing (3) by (2) we get:
\[\large \frac{1500}{700}=\frac{Ae^{35k}}{Ae^{10k}}\ ...........(4)\]
Equation (4) simplifies to:
\[\large \frac{15}{7}=e^{25k}\ .............(5)\]

Answer 2

Taking natural logs of both sides of (5) we get:
\[\large \ln \frac{15}{7}=25k\ .............(6)\]
and solving (6) gives k = 0.0305
Substituting the value of k into (2) we find that the initial size of the culture A = 516.

Answer 3

Thank you

Answer 4

You're welcome :)