### Home > INT3 > Chapter 10 > Lesson 10.2.2 > Problem10-136

10-136.

As a field worker for the World Health Organization, you learn of outbreaks of viral diseases in two different parts of the world. For the next two weeks, you track the number of infected people in each region:

Region A

 Date # people infected June 7 June 10 June 14 June 18 June 21 $120$ $127$ $144$ $157$ $170$

Region B

 Date # people infected June 7 June 10 June 13 June 16 June 19 $22$ $28$ $37$ $48$ $62$
1. For these two weeks, what is the average rate of change in the number of people infected for each region? In which region does it appear the disease is spreading faster?

Recall that the average rate of change is equivalent to the average slope.

2. Considering the situation, what kind of model would be a better choice than average rate of change to represent the outbreak data?

Are the number of infected people initially increasing in a linear fashion?

Outbreaks of disease usually grow exponentially at first.

3. It takes $20$ days to set up an emergency field hospital. You have your biohazard suit and medical supplies all packed, but which part of the world do you fly to? Justify your answer.

Notice that each region's data does not start or extend to the same date.

What is the pattern you can see if each were extended $20$ more days? It may surprise you.

4. Use a regression model to predict how many people will be sick in each region on the day you set up the hospital.

Use June 7 as day 0.

Region A: $y = 117· 1.026^{x}$