Word Problem on Ploynomials

Topic : Ploynomial

Question : A lady three years ago purchased a 1953 corvette roadster for $99000, two years agp she purchased 1929 pierce arrow model 125 for $55000. A year ago purchased a 1909 cadillac model thirty for $65000.
a) let x represent 1 plus the average rate of appreciation. Write a function in terms of x that models the value of the automobiles.
b) If the automobiles appreciate at an average annual rate of 15%, Find the current value of the three automobiles.

Solution :
a) X= 1 + r where r is the average rate of appreciation. Let T(x) represent the total current value of the three cars. T(x) can be expressed as polynomial where the exponents represent the time lapsed after the purchase of each car.
Total Current Value of Cars = Corvette Roadster + Pierce-Arrow + 1909 Cadillac
T(x) = 99,000 x³ + 55,000 x² + 65,000 x
b) Since r=0.15, x = 1 + 0.15 = 1.15. Now evaluate T(x) for x = 1.15.
T(x) = 99,000 x³ + 55,000 x² + 65,000 x
T(1.15) = 99,000(1.15)³ + 55,000(1.15)² + 65,000(1.15)
= 150,566.63 + 72,737.50 + 74,750 = $ 298,054.13
The current value of the three automobiles is $ 298,054.13