Math Problem Statement
Solution
Let’s analyze the problem:
Part (a)
We are given the recursive relation:
We need to find . This is a geometric progression where:
Substitute and :
Let’s calculate this.
Part (b)
We are given the recursive relation:
This is an arithmetic progression. The general formula for an arithmetic progression is:
where is the common difference. Here, .
Substitute and :
Let me compute these values.ations for the given problem
Part (a) calculations
p0_a = 14 # Initial value for part (a) decay_factor = 0.96 # Decay factor t_a = 69 # Time index for part (a) p69 = p0_a * (decay_factor ** t_a)
Part (b) calculations
p0_b = 20 # Initial value for part (b) increment = 0.13 # Increment factor
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Math Problem Analysis
Mathematical Concepts
Sequences
Geometric Progression
Arithmetic Progression
Formulas
General formula for geometric progression: pt = p0 * (common ratio)^t
General formula for arithmetic progression: pt = p0 + t * common difference
Theorems
None explicitly mentioned, but utilizes properties of progressions
Suitable Grade Level
Grades 9-12
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