Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

The equation that represents this situation is y = 5000(0.7)ˣ

An exponential decay is given by:

y = abˣ

where a is the initial value of y, b is the rate of decay and y, x are variables.

Since the culture begins with 5000 cells, hence a = 5000. The cells die by 30% each year, hence b = 100% - 30% = 0.7

The equation is: y = 5000(0.7)ˣ

Therefore the equation that represents this situation is y = 5000(0.7)ˣ

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Step-by-step explanation:

The problem presented is one in which the population of the bacteria  depreciates by a decay factor r every year.

Since it is a decay problem, we use the model:

Initial Population, P=5000

Decay Rate,r=30%=0.3

t=time interval

Therefore, the equation that represents this situation is:

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