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Common Core (Functions)

Common Core for Mathematics

Examples, solutions, and lessons to help High School students learn how to write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

B. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^{t}, y = (0.97)^{t}, y = (1.01)^{12t}, y = (1.2)^{t/10}, and classify them as representing exponential growth or decay.

Common Core: HSF-IF.C.8

The following diagram gives the function for exponential growth and decay. Scroll down the page for more examples and solutions on how to use the exponential growth and decay functions.

**Ex: Exponential Functions: Growth Rate and Growth Factor**

This video explains to to find the growth rate as a decimal and a percent and how to find the growth factor.

**Ex: Exponential Growth Function - Population**

This video explains how to determine an exponential growth function from given information. Then it explains how to determine when a certain population will be reached and when it will double.

**Exponential Function Application (y=ab ^{x}) - Home Values**

This video explains how to determine an exponential function from given data about home values. The annual growth rate is also found.

**Exponential Function Application (y=ae ^{kt}) - Bacteria Growth**

This video explains how to determine an continuous exponential growth function from information given about bacteria growth.

**Exponential Function Application (y=ab ^{x}) - Declining Computer Value**

This video explains how to determine an exponential decay function from given data about the declining value of a computer. The annual rate of change is also found.

**Exponential Function Application (y=ab ^{x}) - Depreciation of a Car**

This video provide an example of how an exponential function can be found to determine the value of a depreciating car. The function is then used to determine the value of a car after t years.

**Exponential Function Application (y=ab ^{x}) - Population Growth of India**

This video provide an example of how an exponential function can be found to determine population. The function is then used to make a prediction about the population in the future.

**Exponential Function Application (y=ab ^{x}) - Population Decline of Chicago**

This video provide an example of how an exponential function can be found to determine population. The function is then used to make a prediction about the population in the future.

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