Thread: Population

how would someone work this out???

In a bacteria growing experiment, a biologist observes that the number of bacteria in a certain culture triples every 4 hours. After 12 hours, it is estimated that there are 1 million bacteria in the culture.
a. How many bacteria were present initially
b. What is the doubling time for the bacteria population?

Originally Posted by runner07

how would someone work this out???

In a bacteria growing experiment, a biologist observes that the number of bacteria in a certain culture triples every 4 hours. After 12 hours, it is estimated that there are 1 million bacteria in the culture.
a. How many bacteria were present initially
b. What is the doubling time for the bacteria population?

We use the exponential growth formula here.



where is the population at time , is the initial population, is the rate of growth, and is time.

(a)
we are told that after 4 hours, the population triples. so if we start with at , we will have when . So let's plug those values into our equation.







So we have,

we are also told that when , the population is 1000000

so we have:



now solve for


once you find , you will have the equation that models this growth, part (b) won't be difficult after that. So find and try part (b) and we'll see how far you get


EDIT: This is my 33th post!!!