Options. You are hired to work for 30 days and you get to choose from one of the following two options. Write equations for how much you have earned by the nth day. 1) You get $1000 on your first day, $2000 on your second day, … So on the nth day you earn n x $1000. 2) You get $0.01 (1 penny on the first day) and each day afterwards the amount in your account doubles. So on day 2 you have $0.02, etc. Which option do you take? If you take option (2) on which day does that option become more profitable than option (1)?
How do I write out the equations for both options?
+130518 With the first option....the total amount that you have earned =
1000 (30)(31)/2 = $465,000
With the second option.....the amount you have earned =
.01[1 - 2^30] / [1 - 2] = $10,737,418.23 ......!!!!
Obviously.....the second one is better
We need to solve this equation for n to find out when the second is better than the first
1000(n)(n + 1) / 2 < .01[1 - 2^n] / [ 1 - 2]
This is best solved using an online app....WolframAlpha shows the answer to be about 24.98 days......so .....option 2 is better in about 25 days
