This next example is long but will illustrate the key difference between EXPONENTIAL FUNCTIONS and LINEAR FUNCTIONS. Problem 2 WORKED EXAMPLE – DOLLARS & SENSE On December 31st around 10 pm, you are sitting quietly in your house watching Dick Clark's New Year's Eve special when there is a knock at the door. Wondering who could possibly be visiting at this hour you head to the front door to find out who it is. Seeing a man dressed in a three-piece suit and tie and holding a briefcase, you cautiously open the door. The man introduces himself as a lawyer representing the estate of your recently deceased great uncle. Turns out your uncle left you some money in his will, but you have to make a decision. The man in the suit explains that you have three options for how to receive your allotment. Option A: $1000 would be deposited on Dec 31st in a bank account bearing your name and each day an additional $1000 would be deposited (until January 31st). Option B: One penny would be deposited on Dec 31st in a bank account bearing your name. Each day, the amount would be doubled (until January 31st). Option C: Take $30,000 on the spot and be done with it. Given that you had been to a party earlier that night and your head was a little fuzzy, you wanted some time to think about it. The man agreed to give you until 11:50 pm. Which option would give you the most money after the 31 days??? A table of values for option A and B are provided on the following page. Before you look at the values, though, which option would you select according to your intuition? Without "doing the math" first, I would instinctively choose the following option (circle your choice): A B C Option A: Option B: $1000 to start + $1000 per day $.01 to start then double each day Note that t= 0 on Dec. 31st Table of input/output values A(t)= Table of input/output values B(t): t = t = time in # of days $ in account after t days time in # of days 0 1000 0 1 2000 1 2 3000 2 3 4000 3 4 5000 4 5 6000 5 $ in account after t days .01 .02 .04 .08 .16 .32