Question

a culture started with 3000 bacteria. after 6 hours, it grew 3600 bacteria. predict how many bacteria will be present after 13 hours

Answer 1

Answer: Hi! in this cases, we usually use a exponential model to describe the growth of the culture.

f(t) = 3000*exp(k*t) where k is a constant.

is easy to see that in t = 0, f(0) = 3000 which is the number at the start.

after 6 hours, we have 3600 bacteria, so:

f(6) = 3000*exp(k*6) = 3600

exp(k*6) = 3600/3000

k = ln(3600/3000)/6 = 0.03

So our exponential is f(t) = 3000*exp(0.03*t)

after 13 hours we get f(13) = 3000*exp(0.03*13) = 4431 total bacteria.

Answer 2

In the case of bacteria, we use the continuous growth equation:
Final=Initial×e∧(r×t)
In other words, the final amount is equal to the initial amount times e to the rate times time. In order to find your rate, you would plug in the numbers as follows:
3600=3000×e∧(6r)
Therefore: r=0.03
Next, you would plug in the r value and 13 hours into the equation to solve for the final amount.
F=3000×e∧(13×0.03)=4,453 bactera after 13 hours