Question

A population of bacteria is initially 2,000. After three hours the population is 1,000.

Assuming this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t)=a(b)t. Report numbers as fractions when necessary, or if using decimals, round to four decimal places.

Answer 1

The population starts at 2000, so a=2000.

We also know that the population in 3 hours is 1000, so we can setup the equation:

2000 b^3 = 1000

This gets us:

b^3 = 1/2

And taking the cube root of both sides gives us:

b ≈ 0.7937005259841

Rounding that to 4 places, we have:

f(t) = 2000 (0.7937)^t