Applications of Exponential and Logarithmic Functions 1 The

Applications of Exponential and Logarithmic Functions 1) The cost of tuition for at four-year public universities has been increasing roughly exponentially for the past 5 years. In 1996, the average cost of tuition was $2,975 per year. By 1997, the figure had risen to $3,211. a) Find the growth factor, b, and explain what it tells you about tuition increases. (remember this can found finding the ratio of exponentials) Find the equation that represents the average cost of tuition at four-year universities as a function of time, with t = 0 corresponding to 1996. b) c) Use this model to estimate the average cost of tuition in 2003 d) Find the year that the average tuition would be $10,000

Solution

a)

growth factor ,b=3211_/2975

growth factor ,b=1.07933

tution fee for the next year will be 1.07933 times that of the present year

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b)

in 1997, t=1997-1996=1

average cost of tution ,AC(t) =((3211-2975)_/(1-0))t + 2975

average cost of tution ,AC(t) =236t + 2975

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c) in 2003 , t=2003-1996 =7

average cost of tution ,AC(7) =(236*7) + 2975

average cost of tution ,AC(7) =4627 $

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d)

AC(t)=10000

=>236t + 2975 =10000

=>t=(10000-2975)_/236

=>t=29.766949

year = 1996+29.766949

year = 2026

in year 2026 average tution fee woulld by $10000