The count in a bateria culture was 400 after 20 minutes and 1400 after 40 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 70 minutes. and When will the population reach 15000.

Question

kropot72 · Answer

$$y(t)=a \times e ^{kt}$$
Where y(t) = value at time "t"
a = value at the start
k = rate of growth (when >0) or decay (when <0)
t = time
To solve this question you need to form two equations using the given data:
$$400=a \times e ^{20k}\ ...........(1)$$
$$1400=a \times e ^{40k}\ .........(2)$$
If you take natural logs of both sides of equations (1) and (2) you will be able to subtract the equations and eliminate the term in a. Then you can solve to find k and then substitute the value of k into equation (1) to find a.