Math Problem Statement

A variety of functions are shown below.

Complete the table to determine the percent rate of change of each function. Choose the correct percent rate of change for each function.

Function 25% Growth 25% Decay 75% Growth 75% Decay

ƒ(x) = 0.25x ƒ(x) = (1 – 0.25)x ƒ(x) = 1.25x ƒ(x) = (1 + 0.25)x ƒ(x) = 0.75x

Solution

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Exponential Decay
Functions
Percent Rate of Change

Formulas

For growth: f(x) = (1 + r)^x, where r is the rate of growth
For decay: f(x) = (1 - r)^x, where r is the rate of decay

Theorems

Exponential Growth and Decay Theorem

Suitable Grade Level

Grades 9-12