7.1.2 What is the connection?

Multiple Representations of Exponential Functions

StandardsA‑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 StandardsF‑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 TableComplete the table for the exponential

equation.

𝑦=20 (3 )𝑥 x y

0

1

2

Graph EquationWrite an equation for the graph without

making a table.