Question

Bacteria X has a relative growth rate of 160 % (under ideal conditions). Some bacteria X are accidentally introduced into some egg salad. Four hours after contamination, there were 45,000 bacteria X in the egg salad. Find the initial number of bacteria X introduced into the egg salad: Estimate the number of bacteria in the food 5 hours after contamination.

Answer 1

6866, 71995

Explanation:

I'm going to assume it has a growth rate of 160% per hour.

Anyways, since after four hours, there were 45,000 Bacteria X in the egg salad, we can write the following function:

`B(h)=P(1.6)^h`, where P represents the initial amount, B(h) represents the total, and h represents the number of hours that has passed. The 1.6 represents the 160% growth rate per hour.

We already know that four hours has passed when the population is 45,000, thus:

`45000=P(1.6)^4`

`P=45000/(1.6)^4`

`P\approx6866.46\approx6866`

So the initial population is around 6866.

After five hours, the number of bacteria will be:

`B(5)=6866(1.6)^5\approx71995`