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
