Problem

(III) Many sailboats are moored at a marina 4.4 $…

02:41

Problem 32 Hard Difficulty

(III) I agree to hire you for 30 days and you can decide between two possible methods of payment: cither $(1) \$ 1000$ a day, or (2) one penny on the first day, two pennics on the scoond day and continue to double your daily pay cach day up to day 30. Use quick estimation to make your decision, and justify it.

Answer

2nd method

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Physics 101 Mechanics

Physics for Scientists and Engineers with Modern Physics

Chapter 1

Introduction, Measurement, Estimating

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Video Transcript

Okay, So our question says that you're agreed toe be hired for 30 days and you can decide between two possible methods of payment either the first method of payment, which you get $1,000 a day every day for the entire 30 days, or the second method of payment in which one penny is what you get on the first day. Two pennies on the second day. And this continues to double, um, and you continue to double your daily pay each day up to 30 days. And it says to use quick as to make estimations to make your decision and then justified the decision that you make. So we're given that the total time will be murdered. Working is 30 days, which I did notice tea. And then the question is, what is the method of payment we should pick? So let's go ahead and calculate how much we would make with the two methods of payment. So the first method of payment says we're going to get $1,000 per day. Well, go ahead, right out How much we'd be getting per day, which is $1,000 and our money sign, um, and this is per day. Well, we know how many days were going to be working. That's 30. So we multiply this by 30 days. Two big Well, quite this by 30 days when we get our total, which is $30,000. Not too bad for 30 days worth of work. Well, let's go ahead and calculate how much we would make the other way. It's dollars to put our dollar sign in there. Okay, So the other way says that we're going to make one penny on our first day, two pennies on our second day, and this is going to continue to double each day. So the equation for this is your first right out How much you're getting on the first day. This is $0.1. Okay? And then you multiply that by two times T to the minus one tea being the number of days that you have gone. And so just a quick reference. If we were to do it for, say, the first day while t would be one, so you would have to raise to the one minus 11 minus one is zero. So you'd have to raise to the zero power. Anything raised to the zero power is just one, so that would equal one. You multiply that by 0.1 and it gives you 0.1 which is what you expect to make on the first day. So this this equation makes sense, so we'll go ahead and plug in 30 for tea. Since that's the total number of days we will have worked. We have 0.1 dollars multiplied by two to the 30 minus one. Just 29. No, right, that's it's legible. 29. Okay, well, if you go ahead and carry out this car calculation, it comes out to be a 5.4 times 10 to the six dollars. Well, 5.4 times 10 to the sixth is over $5,000,000. It's five point $4,000,000. So clearly the second method is the one you would want to go with. You're gonna make a lot more money if you go with the second method. So second method is preferred and box it in

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