3. The population of a certain type of bacteria can be modelled using the exponential equa- tion = B(t) = Boekt, (3) whe

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3 The Population Of A Certain Type Of Bacteria Can Be Modelled Using The Exponential Equa Tion B T Boekt 3 Whe 1 (143.48 KiB) Viewed 34 times

3. The population of a certain type of bacteria can be modelled using the exponential equa- tion = B(t) = Boekt, (3) where B is the number of bacteria at time t (hours) and Bo is the initial number of bacteria. It is known that the bacteria doubles every 10 hours and that it takes 5 days for the bacteria to reach a population of 1 million (106 bacteria). (a) Find the value for k that produces the doubling of bacteria every 10 hours. Give your answer to 4 decimal places. (b) How many bacteria are present at the start of the experiment? Give your answer to the nearest 10 bacteria. (c) At what rate is the bacteria increasing when there are 300 000 bacteria present? Give your answer to the nearest 10 bacteria/hr. (d) There is another population of bacteria which is decaying. This population follows the exponential equation P= Poe-at, (4) Using equations (3) and (4), find the time when the two populations are equal in terms of Po, Bo, k and a. You must show the necessary working to justify your answers.