Problem preview

A-SSE.1.b Warmup M2-009-A05-V03

Interpret quadratic/exponential expressions by treating sub-expressions as meaningful units.

Use a difference table to bracket a solution of f(x) = g(x)

Problem

Interpret \(N=20\cdot~2^5\) as repeated multiplication. Identify the starting value, doubling factor, percent growth per interval, and number of intervals, then compute the total multiplier and \(N\).

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Initial 20; factor 2; +100% each interval; 5 intervals; multiplier 1 + 2 + 2 + 2 + 2 + 2 = 11; N = 220.

Initial 20; factor 2; +500% total by multiplying 100% by 5; 5 intervals; multiplier 6; N = 120.

Initial 20; factor 2; +100% each interval; 5 intervals; multiplier 2⁵ = 32; N = 640.

Initial 20; factor 2; +100% each interval; 5 intervals; multiplier (20 · 2)⁵; N = 102,400,000.

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Curriculum context

Course: Math II
Standard: A-SSE.1.b
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Interpret quadratic/exponential expressions by treating sub-expressions as meaningful units.
Problem type: Use a difference table to bracket a solution of f(x) = g(x)