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 \( \$ 25,000 \) ? \( \$ \square \) (c) According to this model, what is the average salary for a graduate of a college or university where the annual tuition is \( \$ 40,000 \) ? \( \$ \square \) Question Help:
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The rate of growth for this linear model is represented by the coefficient of \( n \), which is \( 0.87 \). This means that for every additional thousand dollars spent on annual tuition, the average mid-career salary increases by approximately \( \$870 \). To find the average salary for a graduate where the annual tuition is \( \$25,000 \), we plug \( n = 25 \) into the model: \[ P_{25} = 0.87(25) + 83,000 = 21,750 + 83,000 = \$104,750 \] So, the average mid-career salary would be approximately \( \$104,750 \). Now, for a graduate where the annual tuition is \( \$40,000 \), we simply substitute \( n = 40 \): \[ P_{40} = 0.87(40) + 83,000 = 34,800 + 83,000 = \$117,800 \] Therefore, the average salary for a graduate at this tuition level would be approximately \( \$117,800 \).