The document discusses writing exponential functions from graphs, stories, and percentages. It provides examples of writing equations from graphs by identifying the y-intercept and growth factor, from stories by finding the starting value and growth/decay factor, and from percentages by converting the percent change to a decimal and using it to find the growth/decay factor. It also shows how to write verbal descriptions for exponential functions based on their equation values.

1. 3.4 Writing Exponential
Functions

2. Writing Functions from Graphs
•Use points from the graph to make a
table.
•Identify y-int (0, a) and growth factor b
•Write equation: y = a(b)x

3. Example 1:
•Write an equation of the function
shown:

4. Example 2:
•Write an equation of the function
shown:

5. You Try!
•Write an equation of the function
shown:

6. Writing Equations from Stories
1. Identify the starting value a and
growth/decay factor b.
2. Write equation y = a(b)x

7. Example 1:
•You bake 100 cookies for a bake sale
and sell half of them every hour.

8. You Try!
•You get four hamsters for Christmas
and the hamster population doubles
every month.

9. Growth/Decay as a %
•When the change is given as a %:
•Write the percent as a decimal  r
▫ (divide by 100)
•For growth: b = 1 + r
•For decay: b = 1 – r

10. Example 2:
•You buy an antique table for $525.
Each year the value increases by 5%.

11. Example 3:
•You buy a new car for $24,000. The
value of the car decreases by 16%
each year.

12. You Try!
•You buy a stereo system for $780.
Each year the value decreases by
6%.

13. Writing Verbal Descriptions
•Use the a and b values from the
equation to write a story for the
function.
•For growth: r = b – 1
•For decay: r = 1 – b
•Then write as a % in the story.

14. Example 4:
• y = 6(2)x

15. Example 5:
• f(t) = 500(1.03)t

16. Example 6:
• g(t) = 90(.75)t

17. You Try!
• Write a story for:
• y = 25(1.2)x
• C(t) = 21500(0.88)t