College, Cars & Interest 1) College When Randall began college, tuition cost him about $2.500 a semester. |Cine year later. the cost had increased 8%. A) Find the cost of a semester's tuition one year after Randall began college. 2) Car When Becky graduated college. she bought a new car for $18,000. One year later. the car had dropped 20% in value. A) B} Complete the table to show how tuition would B) C) D) E} increase if the same trend continuesor, if the cost increases 8% each year from the previous ar's value. Years (x) Tuition costs Explain why this relationship would be exponential (and not linear). Write a function in fix) = ab\" fonn that can be used to model the tuition costs in terms of the number of years (X) since Randall began college. Sketch the graph of this function. and describe the domain and range. 0} D} E) Find the value of Becky's car one year after its purchase. Complete the table to show how the car's value would decrease if the same trend continuesor, if its value decreases 20% each year from the urevious ear's value. Explain why this relationship would be exponential (and not linear). Write a function in fix} = ab" form that can be used to model the car's value in terms of the number of years (x) since its purchase. Sketch the graph of this function. and describe the domain and range. College, Cars & Interest f ( t ) = 2 (1+ + )" In most cases, financial institutions compound interest every month (or, 12 times a year). However, the given formula can be used to determine the value (f(t)) of an investment after t years where interest is compounded n times per year. Use this formula to complete the table for an initial investment of $1,000 with an annual interest rate of 5%. Round answers to the nearest dollar. Compounding f( t) f(5) f(10) Period n Value after t years (Value after (Value after 5 years) 10 years) Annually n = 1 $1,276 (Once a year) Semi-annually n = 2 f(t) = 1,000 (1+ 2.05 )2t (Twice a year) Quarterly (4 times a year) n = 12 Continue the process, but round answers to the nearest cent. f(5) f(10) Compounding f( t) Period n Value after t years (Value after (Value after 5 years) 10 years) Daily Every hour Every minute With your teacher's guidance, write down the formula to use if "interest" is said to accumulate continuously (or, every fraction of every second). With this formula, find the value of the investment with continuously compounded interest after 5 years and 10 years. How do these answers compare to those in the table above