The doubling period of a bacterial population is 15 minutes. At time t=110 minutes, the bacterial population was 50000. What was the initial population at time t=0?

Find the size of the bacterial population after 5 hours.

The initial population is about 310 bacteria.

The size of the bacterial population after five hours is about 325, 058, 560.

Step-by-step explanation:

The exponential function describing growth is given by:

Where A is the amount afterwards, A₀ is the initial amount, r is the rate of growth, t is the amount of time that has passed and d is the time it takes for one cycle (both t and d are minutes in this case).

We are given that the bacteria population doubles after every 15 minutes. Hence, r = 2 and d = 15:

At time t = 110 minutes, the bacterial population was 50,000. Hence:

Solve for A₀:

Hence, the initial population (when t = 0) was about 310.

Thus, our function is:

After five hours, 300 minutes would have passed. Thus:

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step-by-step explanation:

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