Title: |
Exponential Growth and Decay |
URL: |
https://www.ck12.org/c/calculus/differential-equations-representing-growth-and-decay/lesson/Exponential-Growth-and-Decay-CALC/?referrer=concept_details |
Content Source: |
Other
CK-12
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| Type: |
Informational Material
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Overview: |
When the rate of change of the amount of a substance, or a population, is proportional to the amount present at any time, we say that this substance or population is going through either a decay or a growth, depending on the sign of the constant of proportionality. Do you know how to write a differential equation that expresses this condition? This kind of growth or decay, common in nature and in the business world, is called exponential growth or exponential decay and is characterized by rapid change.
This informational material will explain how to find solutions to differential equations that represent rapid change. It will explain real-life applications of these equations, such as radioactive decay and compound interest. There are corresponding videos available. Practice questions with a PDF answer key are provided. |
| Content Standard(s): |
Mathematics
MA2019 (2019)
Grade: 9-12
Mathematical Modeling | 4. Organize and display financial information using geometric sequences to represent compound interest and proportional depreciation, including periodic (yearly, monthly, weekly) and continuous compounding.
a. Explain the relationship between annual percentage yield (APY) and annual percentage rate (APR) as values for r in the formulas A=P(1+r)t and A=Pert. | Mathematics
MA2019 (2019)
Grade: 9-12
Precalculus | 25. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Extend from polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions.
a. Find the difference quotient f(x+Î"x)-f(x)/Î"x of a function and use it to evaluate the average rate of change at a point.
b. Explore how the average rate of change of a function over an interval (presented symbolically or as a table) can be used to approximate the instantaneous rate of change at a point as the interval decreases.
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| Tags:
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continuous compounding, decay, exponential, function, growth, mathematical modeling, precalculus, radioactive, rate of change |
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| Accessibility | Text Resources: Content is organized under headings and subheadings
Video resources: includes closed captioning or subtitles |
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