Question

A culture of 3,000 bacteria quadruples in number every 10 hours. Plt) represents the

population of the bacteria after thours. Which equation best models the growth of
the bacteria?

Answer 1

P(t) = 3000 * 4^(t/10)

Explanation:

There is more than one way to get an exponential function out of the information given. The way the question is worded, however, seems to suggest the following type of answer:

One general form of the exponential function is y = a·bx, where a is the initial value, and b is the growth or decay factor. So right away we can say that a = 2300.

Now for the growth factor. When something is increasing or decreasing by a certain percentage, we are adding or subtracting that percentage to the 100% (which is equal to 1) that exists currently. So here we're increasing by 11%, or 0.11. Then the growth factor b is (1 + 0.11), or 1.11.