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. 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. 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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 6DE
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Transcribed Image Text:Day
1
2
3
4
5
6
7
8
9
10
Pay on this day Total amount paid to date
$0.01
$0.01
$0.02
$0.03
Table 8.2.3: Option 2 payments
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.
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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