Apopulation of bacteria is growing exponentially. at 7: 00 a. m. the mass of the population is 12 mg. five hours later it is 14 mg. (a) what will be the mass of the bacteria after another 5 hours? (b) at 7: 00 p. m. what do we expect the mass to be? (c) what was the mass of the population at 8: 00 a. m.? given your answer, by what percent is the mass of the population increasing each hour? by what percent is it increasing each day?

Answer with Step-by-step explanation:

The exponential growth function is given by

where

is the population of the bacteria at any time 't'

is the population of the bacteria at any time 't = 0'

'm' is a constant and 't' is time after 7.00 a.m in hours

Assuming we start our measurement at 7.00 a.m as reference time  t = 0

Thus we get

Now since it is given after 5 hours the population becomes 14 mg thus from the above relation we get

Thus the population of bacteria at any time 't' is given by

Part a)

Population of bacteria after another 5 hours equals the population after 10 hours from start

Part b)

Population of bacteria at 7:00 p.m is mass after 12 hours

Part c)

Population of bacteria at 8:00 p.m is mass after 1 hour

Part d)

Differentiating the relation of population with respect to time we get

Thus we can see that the percentage increase varies with time initially the percentage increase is 37.2% but this percentage increase increases with increase in time

Part 4)

Since there are 24 hours in 1 day thus the percentage increase in the population is

Thus there is an increase of 110.42% in the population each day.

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step-by-step explanation: