A colony of bacteria is growing in a petri dish which has a maximum capacity of

Question

A colony of bacteria is growing in a petri dish which has a maximum capacity of 80mg. The mass of bacteria is increasing at a rate given by the logistic equation. Initially there is 2mg of bacteria and the rate of increase is 1mg per day.

Write down the logistic equation satisfied by the mass, m. m =

When will the mass of bacteria be 40mg? number of days =

A colony of bacteria is growing in a petri dish which has a maximum capacity of 80mg. The mass of bacteria is increasing at a rate given by the logistic equation. Initially there is 2mg of bacteria and the rate of increase is 1mg per day. Write down the logistic equation satisfied by the mass, m. m 80/(39en(-kt)+1 When will the mass of bacteria be 40mg? number of days What is the mass (in GRAMS of bacteria 10 days after the mass was 2mg? mass grams

Explanation / Answer

Let the m' be the mass of bacteria after n days.

Initially there is 2mg of bacteria and the rate of increase is 1mg per day.

m' = 2 + 1*n (Inital mass + 1mg per day * no of days)

m' = 2 + 1*n ................ (1)

2. Here m' is given as 40 mg

n can be calculated by eqn. (1)

m' = 2 + 1*n
40 = 2 + n
n = 38 days

3.
Initially there is 2mg of bacteria.. so (1) holds

m'= 2+n
m'=2+10=12 mg = 12/1000 gms =0.012 gms

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