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4. In a limited environment where A is the maximum number of bacteria supportable by the environment, the rate of bacterial growth is jointly proportional to the number present and the difference between A and the number present. Suppose 1 million bacteria is the maximum number supportable by the environment and the rate of growth is 61 bacteria per minute when there are 1000 bacteria present.

(a) Express the rate of bacterial growth as a function of the number of bacteria present.

(b).find the rate of growth when there are 100,000 bacteria present ​