Question

Bacteria X has a growth rate of 160 % per hour. Some amount of bacteria X are accidentally introduced into some egg salad. Two 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 3 hours after contamination.

Answer 1

To find the initial number of bacteria X introduced into the egg salad, use exponential growth formula. Estimate the number of bacteria in the food 3 hours after contamination using the same formula.

Step-by-step explanation:

To find the initial number of bacteria X introduced into the egg salad, we can use exponential growth formula. In this case, the growth rate is 160% per hour. Let's assume the initial number of bacteria X is 'N', and after two hours, there were 45,000 bacteria X in the egg salad. So, after two hours, the population size would be N * (1 + (160/100))^2 = 45,000. From this, we can solve for N to find the initial number of bacteria X.

To estimate the number of bacteria in the food 3 hours after contamination, we can use the same exponential growth formula. We know the initial number of bacteria X (which we found earlier) and the growth rate. Plugging these values into the formula, we can calculate the population size after 3 hours.

Answer 2

Answer: initial number: 17,773

3 hours after contamination: 72,798

Step-by-step explanation:

We know that the growth rate is 160% (or 1.6 in decimal form)

This means that if we start with a quantity A initially, after one hour we will have a quantity A*1.6 of bacteria.

After another hour, we will have a quantity (A*1.6)*1.6 = A*1.6^2 of bacteria.

Then we can model this with an exponential equation:

B(t) = A*1.6^t

where t is the time in hours.

We know that when t = 2, we have:

45,000 = A*1.6^2

Here we can solve it for A, which is the initial number of bacteria X.

A = 45,500/(1.6^2) = 17,773,4

That we can round down, because we need whole numbers, so the initial number of bacteria X in the egg salad is A = 17,773

If we want to find the number of bacteria 3 hours after the contamination, we need to use t = 3.

B(t) = 17,773*1.6^t

B(3) = 17,773*1.6^3 = 72,798.2

That again, we need to round to the next whole number, so we round down.

B(3) = 72,798