Need help with Exponential Functions

You're sitting in math class, minding your own business, when in walks a Bill Gates kind of guy - the real success story of your school. He's made it big, and now he has a job offer for you. He doesn't give too many details, mumbles something about the possibility of danger. He's going to need you for 30 days, and you'll have to miss school. (Won't that just be too awful?) And you've got to make sure your passport is current. (Ok - no big deal). But do you ever sit up at the next thing he says: You'll have your choice of two payment options: 1. One cent on the first day, two cents on the second day, and double your salary every day thereafter for the thirty days; or 2. Exactly $1,000,000. (That's one million dollars!) You jump up out of your seat at that. You've got your man, Bill, right herel You'll take that million. You are there. And off you go on this dangerous million-dollar mission. So how smart was this guy? Did you make the best choice? Before we decide for sure, let's investigate the first payment option. Complete the table for the first week's work. So, after a whole week you would have only made That's pretty awful, all right. There's no way to make a million in a month at this rate. Right? Let's check out the second week. Complete the second table. Well, you would make a little more the second week; at least you would have made a total of for 2 weeks of work. But there's still a big difference between this salary and $1,000,000. What about the third week? We're getting into some serious money here now, but still nowhere even close to a million. And there's only 10 days left. So it looks like the million dollars is the best deal. Of course, we suspected that all along. Halditl Look what has happened. What's going on here? This can't be right. This is amazing. Look how fast this pay is growing. Let's keep going. I can't wait to see what the total will be. In 30 days, it increases from 1 penny to over dollars. That is absolutely amazing! Explain what should be the best choice of pay for the 30 day period. Explain what type of function is modeled in the first option. Determine the initial amount and multiplier used to determine each day's pay, where t=0 would be day 1 (fill in the blanks): A(t)=1t