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Population decay where rate of decay is proportional to the population present

Step-by-step explanation:

Given that

Here N (t) represents the population or amount of bacteria present at time t.

N0 represents the initial population or N(0)

Since e has negative exponent, there is population decay and not expansion.

l, the coefficient of t in the exponent of e is the factor which represents the rate of decay

Whenever decay is proportional to the population present at that time, we get this equation.

N'=-lN

Separate the variables and integrate to get