Math Problem Statement
Performance Task 13 Donation for a Cause
- You are running a foundation for street children. Mr. Felipe Cortejos, a rich benefactor, offers two options for his donations: Option A: To give Php 1 000 on day 1, Php 999 on day 2, Php 998 on day 3, with the process to end after 1 000 days. Option B: To give Php 1 on day 1, Php 2 on day 2, Php 4 on day 3, for 1 000 days. You have to tell him today which option you want to take. Which of the two options results in more money for the foundation? Show your computations. Which option are you going to take?
Solution
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequence
Geometric Sequence
Summation of Series
Exponential Growth
Formulas
Sum of an arithmetic sequence: Sn = (n/2) * (a1 + an)
Sum of a geometric sequence: Sn = a1 * (1 - r^n) / (1 - r)
Theorems
Arithmetic Series Theorem
Geometric Series Theorem
Suitable Grade Level
Grades 9-12
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