Transcript Exponential functions

7.1.2
What is the connection?
Multiple Representations of Exponential Functions
Standards
 A-CED.1. Create equations in one variable and use them to
solve problems.
 F-IF.7e. Graph exponential functions, showing intercepts and
end behavior.
 A-CED.2. Create equations in two or more variables to
represent relationships between quantities; graph equations
on coordinate axes with labels and scales.
 F-IF.6. 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.
More Standards
 F-IF.8b. Use the properties of exponents to interpret
expressions for exponential functions.
 F-LE.1c. Recognize situations in which a quantity grows or
decays by a constant percent rate per unit interval relative to
another.
 F-LE.2. Construct exponential functions given a graph, a
description of a relation-ship, or two input-output pairs
(include reading these from a table).
 F-LE.5. Interpret the parameters in a linear or exponential
function in terms of a context.
Many exponential equations are in the
form y=abx.
 What does the a represent in this equation?
 What does b represent?
Table
Equation
 Arnold dropped a ball during a bouncing ball activity and
recorded its height in a table. Part of his table is shown at
right. Write an equation that represents his data.
Equation
Situation
 A major technology company, ExpoGrow, is growing
incredibly fast. The latest prospectus (a report on the
company) said that so far, the number of employees, y, could
be found with the equation y = 3(4)x , where x represents
the number of years since the company was founded.
 How many people founded the company?
 How can the growth of this company be described?
Table
Situation
 A computer virus is affecting the technology center in such a
way that each day, a certain portion of virus-free computers
is infected. The number of virus-free computers is recorded
in the table at right.
 How many computers are in the technology center?
 What portion of virus-free computers is infected each day?
 How many computers will remain virus-free at the end of
the third day?
Equation
Table
 Complete the table for the exponential equation.
𝑦 = 20 3
𝑥
x
0
1
2
y
Graph
Equation
 Write an equation for the graph without making a table.