A college student wishes to compare tuition fee increases during the period 1999 to 2009 to the general increase in the cost of living. Tuition increased from $350 per course in the 1999/2000 academic year to $495 per course in the 2009/10 academic year. The CPI rose from 92.9 in mid-1999 to 115.1 in mid-2009.

What would the tuition fee per course have been in the 2009/10 year if tuition increases had merely kept pace with inflation during the 10 years?

To calculate the tuition fee per course in the 2009/10 year if tuition increases had merely kept pace with inflation during the 10 years, you need to determine the inflation rate over the period.

1. Calculate the percentage increase in the Consumer Price Index (CPI) over the 10-year period:
Percentage increase = ((Ending CPI - Starting CPI) / Starting CPI) * 100
= ((115.1 - 92.9) / 92.9) * 100

2. Calculate the average annual inflation rate:
Average annual inflation rate = Percentage increase / Number of years
= (percentage increase) / 10

3. Calculate the compounded inflation factor:
Compounded inflation factor = (1 + (average annual inflation rate / 100))^10

4. Calculate the adjusted tuition fee per course:
Adjusted tuition fee per course = Starting tuition fee per course * compounded inflation factor

Substituting the given values,

Starting CPI = 92.9
Ending CPI = 115.1
Starting tuition fee per course = $350

Step 1: Calculate the percentage increase in CPI:
Percentage increase = ((115.1 - 92.9) / 92.9) * 100

Step 2: Calculate the average annual inflation rate:
Average annual inflation rate = (percentage increase) / 10

Step 3: Calculate the compounded inflation factor:
Compounded inflation factor = (1 + (average annual inflation rate / 100))^10

Step 4: Calculate the adjusted tuition fee per course:
Adjusted tuition fee per course = Starting tuition fee per course * compounded inflation factor

Now, let's compute the steps:

Step 1: Calculate the percentage increase in CPI:
Percentage increase = ((115.1 - 92.9) / 92.9) * 100
= (22.2 / 92.9) * 100
= 23.9%

Step 2: Calculate the average annual inflation rate:
Average annual inflation rate = (23.9%) / 10
= 2.39%

Step 3: Calculate the compounded inflation factor:
Compounded inflation factor = (1 + (2.39% / 100))^10
= (1 + 0.0239)^10
= 1.2624

Step 4: Calculate the adjusted tuition fee per course:
Adjusted tuition fee per course = $350 * 1.2624
= $442.84

Therefore, the tuition fee per course in the 2009/10 academic year, if tuition increases had merely kept pace with inflation during the 10 years, would have been approximately $442.84.

To determine what the tuition fee per course would have been in the 2009/10 year if it had kept pace with inflation, we can use the Consumer Price Index (CPI) as a measure of inflation.

First, we need to calculate the percentage increase in CPI over the 10-year period. To do this, we subtract the CPI of the starting year (92.9) from the CPI of the ending year (115.1), and then divide the result by the CPI of the starting year.

Percentage change in CPI = ((CPI of ending year - CPI of starting year) / CPI of starting year) * 100
= ((115.1 - 92.9) / 92.9) * 100

Next, we need to calculate the percentage increase in tuition fees over the same 10-year period. To do this, subtract the initial tuition fee ($350) from the final tuition fee ($495), and divide the result by the initial tuition fee.

Percentage change in tuition fees = ((Final tuition fee - Initial tuition fee) / Initial tuition fee) * 100
= ((495 - 350) / 350) * 100

Now, we know that if the tuition fees had kept pace with inflation, the percentage change in tuition fees would be equal to the percentage change in CPI.

So, we can set up the following equation:

((495 - 350) / 350) * 100 = ((115.1 - 92.9) / 92.9) * 100

To solve for the final tuition fee, we can rearrange the equation as follows:

Final tuition fee = (Initial tuition fee * ((115.1 - 92.9) / 92.9)) + Initial tuition fee

Now we can calculate the final tuition fee:

Final tuition fee = (350 * ((115.1 - 92.9) / 92.9)) + 350

Plug in the values and calculate:

Final tuition fee = (350 * (22.2 / 92.9)) + 350
= (350 * 0.2391) + 350
= 83.67 + 350
= $433.67 (rounded to the nearest cent)

Therefore, if tuition fees had kept pace with inflation during the 10-year period, the tuition fee per course in the 2009/10 academic year would have been approximately $433.67.