3 Questions
Explain the difference between linear functions and exponential functions in terms of their growth patterns over equal intervals.
Linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals.
How can you recognize situations in which one quantity changes at a constant rate per unit interval relative to another?
You can recognize these situations by observing that one quantity changes at a constant rate per unit interval relative to another.
In what situations does a quantity grow or decay by a constant percent rate per unit interval relative to another?
A quantity grows or decays by a constant percent rate per unit interval relative to another in certain situations, which should be recognized.
Study Notes
Linear Functions vs. Exponential Functions
- Linear functions exhibit a constant rate of change over equal intervals, resulting in a steady, proportional increase or decrease.
- Exponential functions display a constant percentage rate of change over equal intervals, leading to accelerated growth or decay.
Recognizing Constant Rate of Change
- A quantity changes at a constant rate per unit interval relative to another when the difference in values remains the same over equal intervals.
- This is characteristic of linear functions, where the rate of change is constant and predictable.
Recognizing Constant Percent Rate of Change
- A quantity grows or decays by a constant percent rate per unit interval relative to another when the ratio of values remains the same over equal intervals.
- This is characteristic of exponential functions, where the rate of change is proportional to the current value and results in accelerating growth or decay.
- Situations involving constant percent rate of change include population growth, compound interest, and chemical reactions.
Test your knowledge of linear and exponential functions with this quiz! Learn to distinguish between situations that can be modeled with each type of function, verify their growth patterns, and recognize changes in quantities over equal intervals.
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