Question

A bacteria colony with a population of 250,000 is given an antibiotic that kills half of the colony each day. Write the exponential

function that models this situation.

Answer 1

Let P(t) be the population of the bacteria colony after t days. We know that each day, the population is reduced by half, so we can write:
P(t) = P(0) * 0.5^t
where P(0) is the initial population, which is 250,000.
Substituting P(0) into the equation, we get:
P(t) = 250,000 * 0.5^t
This is the exponential function that models the situation. It shows how the population of the bacteria colony decreases over time as a result of the antibiotic treatment.