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.
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.
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=abt) - 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.
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.
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