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:

the least common denominator is 40

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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