Question

There are 70000 bacteria present in a culture. An Antibiotic is introduced to the culture and the number of bacteria is reduced by half every four hours.

Answer 1

y = 70000(0.5)^(x/4), where x equals the number of hours.

(Attached is an image with the equation properly formatted.)

The function for exponential decay is y = a(1 - b)^x, where y is the final amount, a is the starting amount, b is the decay percentage in decimal form.

So, just fill in the values.

y = 70000(1 - 0.5)^x

y = 70000(0.5)^x

In this case however, x represents the number of sets of four hours, so we should probably divide x by 4 to make x represent the number of hours.

y = 70000(0.5)^(x-4)