5. There is an old question that is often used to introduce the power of geometric growth. Here is one version. Suppose you are hired for a one month (30 days, working every day) job and are given two options to be paid. Option 1. You can be paid $500 per day or Option 2. You can be paid 1 cent the first day, 2 cents the second day, 4 cents the third day, 8 cents the fourth day, and so on, doubling the amount you are paid each day. a. How much will you be paid for the job in total under Option 1? b. Complete Table 8.2.3 to determine the pay you will receive under Option 2 for the first 10 days. Table 8.2.3. Option 2 payments Day Pay on this day Total amount paid to date 1 $0.01 $0.01 $0.03 2 $0.02 3 4 5 6 7 8 9 10 c. Find a formula for the amount paid on day n, as well as for the total amount paid by day n. Use this formula to determine which option (1 or 2) you should take.
5. There is an old question that is often used to introduce the power of geometric growth. Here is one version. Suppose you are hired for a one month (30 days, working every day) job and are given two options to be paid. Option 1. You can be paid $500 per day or Option 2. You can be paid 1 cent the first day, 2 cents the second day, 4 cents the third day, 8 cents the fourth day, and so on, doubling the amount you are paid each day. a. How much will you be paid for the job in total under Option 1? b. Complete Table 8.2.3 to determine the pay you will receive under Option 2 for the first 10 days. Table 8.2.3. Option 2 payments Day Pay on this day Total amount paid to date 1 $0.01 $0.01 $0.03 2 $0.02 3 4 5 6 7 8 9 10 c. Find a formula for the amount paid on day n, as well as for the total amount paid by day n. Use this formula to determine which option (1 or 2) you should take.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. There is an old question that is often used to introduce the power of
geometric growth. Here is one version. Suppose you are hired for a one month
(30 days, working every day) job and are given two options to be paid.
Option 1.
You can be paid $500 per day or
Option 2.
You can be paid 1 cent the first day, 2 cents the second
day, 4 cents the third day, 8 cents the fourth day, and
so on, doubling the amount you are paid each day.
a. How much will you be paid for the job in total under Option 1?
b. Complete Table 8.2.3 to determine the pay you will receive under Option
2 for the first 10 days.
Table 8.2.3.
Option 2 payments
Day Pay on this day Total amount paid to date
1
$0.01
$0.01
$0.03
2
$0.02
3
4
7
8
10
c. Find a formula for the amount paid on day n, as well as for the total
amount paid by day n. Use this formula to determine which option (1 or 2)
you should take.
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