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Answer:
3125 bacteria.
Step-by-step explanation:
We can write an exponential function to represent the situation.
We know that the current population is 100,000.
The population doubles each day.
The standard exponential function is given by:
Since our current population is 100,000, a = 100000.
Since our rate is doubling, r = 2.
So:
We want to find the population five days ago.
So, we can say that t = -5. The negative represent the number of days that has passed.
Therefore:
However, we dealing within this context, we really can't have negative days. Although it works in this case, it can cause some confusion. So, let's write a function based on the original population.
We know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, our function is:
After 5 days, we reach the 100,000 population. So, when t = 5, P(t) = 100000:
And solving for A, we acquire:
So, our function in terms of the original day is:
So, it becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.