In 1983, the tuition per term at the University of Oregon was $321. There were three terms per year. In the year 2005, the cost of tuition at the University of Oregon is $5853 per year, or $1951 per term. This growth in the cost of tuition can be modeled by an exponential function: y = a(b)x. The variable y represents the cost of tuition per term, and the variable x corresponds to the number of years that have passed since the initial year. To find this exponential function, make the initial year 1983. During the year 1983, zero years had passed since the initial year and the cost of tuition per term was $321, making y=321 and x=0. When these numerical values substitute for the variables, the equation is 321 = a(b)0. Owing to the fact that any nonzero real number with a zero exponent is equal to 1, (b)0=1. The equation can be simplified to 321=a(1), so 321= a. Since a is a constant, a will always equal 321 in this equation, regardless of the values of the variables. During the year 2005, 22 years have passed since the initial year and the cost of tuition at the University of Oregon is $1951 per term, making x=22 and y=1951. Upon the substitution of the numerical values for the variables, the equation is 1951=321(b)22. By division, b22= (1951/321). b=22√ (1951/321). Since b is a constant, b will always equal 22√ (1951/321), regardless of the values of the variables. Now that both constants have been obtained, an exponential equation expressing the cost of tuition per term at the University of Oregon in terms of the number of years that have passed since 1983 can be made: y =…
