Data on annual tuition and average mid-career salary of graduates of a certain degree program are collected from a number of universities and colleges. The result of the data collection is the linear model \( P_{n}=0.87 n+83,000 \) where \( n \) annual tuition and \( P_{n} \) is the average mid-career salary of graduates, both in thousands of dollars. This model is accurate for annual tuition values between 10 thousand and 40 thousand dollars. (a) What is the rate of growth for this linear model? (b) According to this model, what is the average salary for a graduate of a college or university where the annual tuition is \( \$ 25,000 \) ? \( \$ \) (c) According to this model, what is the average salary for a graduate of a college or university where the annual tuition is \( \$ 40,000 \) ? \( \$ \)

The rate of growth for this linear model is represented by the coefficient of \( n \) in the equation \( P_{n}=0.87 n+83,000 \). This means that for every additional thousand dollars in tuition, the average mid-career salary increases by $870. So, it’s a nice little perk - invest a bit more in tuition, and you could rattle a bigger paycheck down the line! To find the average salary for a graduate from a college or university where the annual tuition is \( \$ 25,000 \), plug \( n = 25 \) into the model: \( P_{25} = 0.87(25) + 83 = 21.75 + 83 = 104.75 \) (in thousands of dollars). Therefore, the average salary would be \( \$ 104,750 \). Not too shabby for investing in your education! For a graduate from a college or university with an annual tuition of \( \$ 40,000 \), plug \( n = 40 \) into the model: \( P_{40} = 0.87(40) + 83 = 34.8 + 83 = 117.8 \) (in thousands of dollars). Thus, the average salary would be \( \$ 117,800 \). That’s some serious earning potential for going the extra mile in tuition!