Question

Researchers recorded that a certain bacteria population declined from 130,000 to 400 in 18 hours. At this rate of decay, how many bacteria was there at 12 hours? Round to the nearest whole number.

Answer 1

Answer:

There were 43,600 bacteria at 12 hours.

Step-by-step explanation:

Rate of Decay

There are several ways to model the rate of decay in a variety of situations. Two of the most-used are exponential decay and linear decay.

The situation expressed in the question talks about a certain bacteria population that went from 130,000 to 400 in 18 hours. This information suggests the linear decay model is being used.

The rate of decay is calculated as the slope of the line.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

We are given the points (0;130,000) and (18;400), thus:

$\displaystyle m=\frac{400-130,000}{18-0}$

m = -7,200

This means the bacteria population decays by 7,200 each hour. Thus, when 12 hours had passed, the bacteria population was:

130,000 - 7,200 * 12 = 43,600

There were 43,600 bacteria at 12 hours.