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Common Core (Functions)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to distinguish between situations that can be modeled with linear functions and with exponential functions.

C. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Common Core: HSF-LE.A.1

**Exponential Growth Function - Bacterial Growth**

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.

Example:

A bacteria culture starting with 200 bacteria grows at a rate proportional to its size. After 3 hours therewill be 900 bacteria.

Express the population after t hours as a function of t?

What will be the population after 6 hours?

When will the population reach 5000?
**Exponential Decay Function - Half Life**

This video explains how to determine an exponential decay function from given information. Then it explains how to determine when a certain level of decay will be reached and how to determine half-life.

Example:

An unknown radioactive element decays into non-radioactive substances. In 30 days the radioactivity of a sample decreases by 12%.

Find the exponential decay model for the decay after t days.

What is the half-life of the sample?

When will a sample 50 mg decay to 10 mg?

**Exponential Growth Application (y=ab**^{t}) - Given Doubling Time

This video explains how to determine an exponential function in the form y=a*b^t given the doubling time. The it determines a population after a given amount of time.

Example:

A bacteria culture initially contains 1200 bacteria and doubles every half hour.

Find the size of the bacterial population after 70 minutes.

Find the size of the bacterial population after 4 hours.

**Exponential Growth Regression Model (Investment Account)**

This video provides an example of how to perform exponential regression on the TI84 graphing calculator and answers a variety of related questions.**
**

Common Core (Functions)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to distinguish between situations that can be modeled with linear functions and with exponential functions.

C. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Common Core: HSF-LE.A.1

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.

Example:

A bacteria culture starting with 200 bacteria grows at a rate proportional to its size. After 3 hours therewill be 900 bacteria.

Express the population after t hours as a function of t?

What will be the population after 6 hours?

When will the population reach 5000?

This video explains how to determine an exponential decay function from given information. Then it explains how to determine when a certain level of decay will be reached and how to determine half-life.

Example:

An unknown radioactive element decays into non-radioactive substances. In 30 days the radioactivity of a sample decreases by 12%.

Find the exponential decay model for the decay after t days.

What is the half-life of the sample?

When will a sample 50 mg decay to 10 mg?

This video explains how to determine an exponential function in the form y=a*b^t given the doubling time. The it determines a population after a given amount of time.

Example:

A bacteria culture initially contains 1200 bacteria and doubles every half hour.

Find the size of the bacterial population after 70 minutes.

Find the size of the bacterial population after 4 hours.

This video provides an example of how to perform exponential regression on the TI84 graphing calculator and answers a variety of related questions.

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