Exponential Functions

Standard: A.CED.1

Essential Questions:

• How do I make a table of values for an exponential function?

• How do I graph an exponential function?

Steps:

• Make a table of values by plugging in x-values (domain) into the function and getting y-values (range). You now have ordered pairs.

• Plot your new ordered pairs on a coordinate plane.

• Draw the curve.

Example 1

• Graph y = 3x by making a table of values.• Use 0, 1, and 2 as your domain.

Example 2

• Graph y = ⅟2x by making a table of values.• Use 0, 1, and 2 as your domain.

Example 3

• Graph y = 2x by making a table of values.• Use 0, 1, and 2 as your domain.

Exponential Growth and Decay:

a = initial amount before measuring growth/decay

r = growth/decay rate (often a percent)x = number of time intervals that have passed

Steps:

• Read the word problem and identify “a”, “r”, and “x”.

• Choose whether the problem is a growth or decay problem – (look for words like increase and decrease).

• Plug values into appropriate formula and solve.

Example 4

• A new TV costs $1200. The value of the TV decreases by 21% each year. Write a model giving the TV’s value after 2 years.

• a = 1200 r = 21% x = 2• Growth or Decay?• Decay• 1200(1-.21)2

• $748.92

Example 5

• Glynn County’s population in 2010 was 70,000. Each year the population increases by 5%. Write a model giving the county’s population in 2015.

• a = 70,000 r = 5% x = 5• Growth or Decay?• Growth• 70,000(1+.05)5

• 89,339

Summarizer:

• How do I graph an exponential function?• Make a table of values

Assignment:

• worksheet