Scientists are researching a contagious disease. They found that, on average, each person who is infected transmits the disease to 0.03 other people within one year. Currently, there are 3,000 infected people in the country. Use Excel or another spreadsheet application to find out (1) how many people will contract the disease each year over the next decade, and (2) how many infected people will there be each year if no medication is administered. (Do not worry: there is a medication for this disease.) "Currently" means in the first year of your calculation. Calculate for the next nine years. Explain why this is a model¬ing problem. What is your model in the spreadsheet?

Hint: People who were sick in the beginning of year remain to be sick and may transmit the disease next year.

To solve this problem, we can use a spreadsheet application like Excel to create a model that calculates the number of people who contract the disease each year and the number of infected people over the next decade.

Here's how we can set up the model in Excel:

Step 1: Create a new spreadsheet and label the columns as follows: Year, Infected People, New Infections, Total Infections.

Step 2: In the first row under the Year column, enter 1 to represent the current year.

Step 3: In the first row under the Infected People column, enter 3,000 to represent the current number of infected people.

Step 4: In the first row under the New Infections column, we'll use a formula to calculate the number of new infections. In cell C2, enter the formula "=B2*0.03", where B2 represents the number of infected people in that year and 0.03 represents the average number of people each infected person transmits the disease to.

Step 5: In the first row under the Total Infections column, we'll use a formula to calculate the total number of infected people each year. In cell D2, enter the formula "=B2+C2", where B2 represents the number of infected people at the beginning of the year and C2 represents the number of new infections.

Step 6: Copy the formulas in cells C2 and D2 and paste them into the cells below for the subsequent years. For example, you can select cells C2 and D2, then drag the fill handle (the small square in the bottom-right corner of the selected cell) down to copy the formulas to cells C3 and D3 for the second year, and so on.

Step 7: Repeat steps 2-6 for the next nine years, updating the year and the number of infected people in each year.

After completing these steps, you will have a spreadsheet model that calculates the number of people who contract the disease each year and the number of infected people over the next decade.

Based on this model, you can analyze the results to answer the given questions:

1) To determine how many people will contract the disease each year over the next decade, you can sum up the new infections for each year. In Excel, you can use the SUM function to calculate the total number of new infections over the ten-year period.

2) If no medication is administered, you can simply observe the total number of infected people each year from the Total Infections column in the spreadsheet model.

This is a modeling problem because we are using a mathematical model to simulate the spread of the disease over time. By setting up formulas and updating the values each year, we can observe the progression of the disease and make predictions about the number of infections. The model takes into account the rate of transmission, the number of infected people at the start of each year, and the accumulation of new infections over time.

To calculate the number of people who will contract the disease each year over the next decade, and the number of infected people each year if no medication is administered, we can use a spreadsheet application like Excel.

Here's a step-by-step explanation:

1. Open a new spreadsheet in Excel.

2. In the first column, label the rows from 0 to 10 with the headings "Year."

3. In the second column, label the rows from 0 to 10 with the heading "Infected."

4. Assign the value 3,000 to cell B1 (Year 0, Infected 0).

5. Now, we will use a formula to calculate the number of newly infected people each year. In cell B2, enter the formula "=B1 * 0.03" and press Enter. This formula multiplies the number of infected people in the previous year by the transmission rate of 0.03 to calculate the new infections.

6. Copy the formula from cell B2 and paste it down to cells B3 through B10. This will calculate the number of new infections for each subsequent year.

7. To calculate the cumulative number of infected people each year, we will add the number of new infections to the previous year's total. In cell C2, enter the formula "=B2 + B1" and press Enter.

8. Copy the formula from cell C2 and paste it down to cells C3 through C10. This will calculate the total number of infected people for each subsequent year.

9. Now, you will have the calculations for both the number of people contracting the disease each year (column B) and the number of infected people each year (column C).

10. Finally, to answer the first part of the question, you can add up the total number of people contracting the disease over the next decade by summing up the values in the "Infected" column (column B) for years 1 to 10. For example, in a new cell, you can use the formula "=SUM(B2:B10)" to calculate the sum.

11. For the second part of the question, the number of infected people each year if no medication is administered is already calculated in column C. You can use the same method as in step 10 to find the total number of infected people over the next decade, by summing up the values in the "Infected" column (column C) for years 1 to 10.

This is a modeling problem because it involves using a mathematical model to simulate the spread of a disease over time. The model assumes that each infected person transmits the disease to 0.03 other people within one year. By using a spreadsheet application, we can easily update and calculate the number of infected people each year based on this transmission rate.

The model in the spreadsheet involves using formulas to calculate the number of newly infected people each year and the cumulative number of infected people. The formula "=B1 * 0.03" calculates the new infections, and the formula "=B2 + B1" adds the new infections to the previous year's total. By copying and pasting these formulas for subsequent years, we can track the spread of the disease over the next decade.