The following table gives the average number of students per computer in public schools for the school years that ended in 1985 through 2002. Let x be the number of years past 1980. Find an exponential model for these data. Round your answer to three decimal places.

Source: Quality Education Data, Inc., Denver, Colorado

A)
B)
C)
D)
E)

Question

The following table gives the average number of students per computer in public schools for the school years that ended in 1985 through 2002. Let x be the number of years past 1980. Find an exponential model for these data. Round your answer to three decimal places.

Source: Quality Education Data, Inc., Denver, Colorado

Source: Quality Education Data, Inc., Denver, Colorado
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A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The general form of an exponential function is y=a*b^x, where a and b are constants. We can use linear regression to find values for a and b that best fit the data. Taking the natural logarithm of both sides of the exponential model we get ln(y) = ln(a) + ln(b)*x. We can now use linear regression on the new data set: (x, ln(y)). The slope of the line of best fit will be ln(b), and e^(intercept) will be a. Using a calculator, we find that the exponential model that best fits the data is y = 14.463e^(-0.036x). Rounded to three decimal places, this is the same as choice C.

The Following Table Gives the Average Number of Students Per