Why It Matters: Exponential and Logarithmic Equations and Models
Where are applications of exponential and logarithmic functions found?
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Amount of sample (g) | 100 | 50 | 25 | 12.5 | 6.25 |
Time (years) | 0 | 5730 | 11,460 | 17,190 | 22,920 |
- How do you develop a model for the decay of carbon-14?
- How can you use the model to determine the amount of carbon-14 that remains after any number of years?
- What would a graph of the decay of carbon-14 look like?
Learning Objectives
Logarithmic Properties
- Use power, product, and quotient rules to expand and condense logarithms
- Use the change-of-base formula for logarithms
Exponential and Logarithmic Equations
- Use like bases to solve exponential equations
- Use logarithms to solve exponential equations
- Use the definition of a logarithm to solve logarithmic equations
- Use the one-to-one property of logarithms to solve logarithmic equations
- Solve applied problems involving exponential and logarithmic equations
Exponential and Logarithmic Models
- Model exponential growth and decay
- Use Newton’s Law of Cooling
- Use logistic-growth models
- Choose an appropriate model for data
- Express an exponential model in base
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