1. Bell Ringer Mrs. Rivas 𝒙 𝟑 𝒚 𝟗 𝟐𝒙 𝟑 𝒚 𝒙 𝟐 𝟑𝟔
Ida S. Baker H.S.
Bell Ringer
Directions: Simplify each radical expression. Show your work.
𝒙 𝟑 𝒚 𝟗
1. 𝑥 𝑦 −
1. ____________
𝟐𝒙 𝟑 𝒚
𝑥 𝑥 𝑦 2
2. ____________
𝒙 𝟐
3. 𝑥
3. ____________ 𝟑𝟔
4. −
4. ____________

2. 𝒚=𝒂 𝒃 𝒙 Exploring Exponential Models Mrs. Rivas Exponential function
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
Objective: To model exponential growth and decay.
Exponential function
𝒚=𝒂 𝒃 𝒙
𝒂≠𝟎
𝒃>𝟎
𝒙 is the independent
variable, with domain the set of all real numbers.
𝒃≠𝟏
𝒃=𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕

3. Exploring Exponential Models
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
Example # 1
Graphing an exponential function. A
What is the graph of 𝑦= 2 𝑥 ?
Step 1: Make a table of values.
Step 2: Plot and connect the points. 𝒙
𝟐 𝒙 𝒚 𝟖
𝟏 𝟏𝟔 −𝟒
𝟐 −𝟒
=𝟎.𝟎𝟔𝟐𝟓
𝟏 𝟖 −𝟑
𝟐 −𝟑
=𝟎.𝟏𝟐𝟓 𝟔
𝟏 𝟒 −𝟐
𝟐 −𝟐
=𝟎.𝟐𝟓 𝟒
𝟏 𝟐 −𝟏
𝟐 −𝟏
=𝟎. 𝟓 𝟎
𝟐 𝟎 𝟏 𝟐 𝟏
𝟐 𝟏 𝟐 𝟐
𝟐 𝟐 𝟒 𝟎 −𝟒 −𝟐 𝟐 𝟒 𝟑
𝟐 𝟑 𝟖

4. Exploring Exponential Models
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
Example # 1
Graphing an exponential function.
What is the graph of 𝑦= 𝑥 ? B
Step 1: Make a table of values.
Step 2: Plot and connect the points. 𝒙
𝟏 𝟐 𝒙 𝒚 𝟖 −𝟑
𝟏 𝟐 −𝟑
𝟐 𝟑 =𝟖
𝟏 𝟐 −𝟐 −𝟐
𝟐 𝟐 =𝟒 𝟔
𝟏 𝟐 −𝟏 −𝟏
𝟐 𝟏 =𝟐
𝟏 𝟐 𝟎 𝟎
𝟐 𝟎 =𝟏 𝟒 𝟏
𝟏 𝟐 𝟏
𝟏 𝟐 =𝟎.𝟓
𝟏 𝟐 𝟐
𝟏 𝟒 =𝟎.𝟐𝟓 𝟐 𝟐
𝟏 𝟐 𝟑 𝟑
𝟏 𝟖 =𝟎.𝟏𝟐𝟓
𝟏 𝟐 𝟒
𝟏 𝟏𝟔 =𝟎.𝟎𝟔𝟐𝟓 𝟒 𝟎 −𝟒 −𝟐 𝟐 𝟒

5. Exploring Exponential Models
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
You Do It
Graphing an exponential function.
What is the graph of each function?
𝒚= 𝟏 𝟑 𝒙 A
𝒚=𝟐 𝟑 𝒙 B

6. Exploring Exponential Models
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
Two types of Exponential Behavior
As the value of 𝒙 increases, the value of 𝒚 decreases approaching zero.
As the value of 𝒙 increases, the value of 𝒚 increases.
Asymptote: is a line that a graph approaches, but never touches the line.

7. 𝒚=𝒂 𝒃 𝒙 Exploring Exponential Models Mrs. Rivas
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
Two types of Exponential Behavior
𝒚=𝒂 𝒃 𝒙
Exponential Decay
Exponential Growth
𝒂>𝟎
𝒂>𝟎
𝟎<𝒃<𝟏
𝒃>𝟏
Domain: all real number
Range: 𝑦>0
y-intercept = (0,𝑎)
Asymptote: 𝑦=0

8. Exploring Exponential Models
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
Example # 2
Identifying Exponential Growth and Decay.
Identify each function as an example of exponential growth or decay. What is the y-intercept? A
𝒚=𝟏𝟐 𝟎.𝟗𝟓 𝒙 B
𝒚=𝟎.𝟐𝟓 𝟐 𝒙
𝒚=𝒂 𝒃 𝒙
𝒚=𝒂 𝒃 𝒙
Since 𝟎<𝒃<𝟏, then the function represents an exponential decay.
Since 𝒃>𝟏, then the function represents an exponential growth.
y-intercept =(𝟎,𝒂)
y-intercept =(𝟎,𝒂)
=(𝟎,𝟏𝟐)
=(𝟎,𝟎.𝟐𝟓)

9. Exploring Exponential Models
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
Example # 2
Identifying Exponential Growth and Decay.
Identify each function as an example of exponential growth or decay. What is the y-intercept? C
You put $1,000 into a college savings account for four years. The account pays 5% interest annually.
The amount of money in the bank grows by 5% annually. It represents the exponential growth.
y-intercept: $1,000, which is the dollar value of the initial investment.

10. Exploring Exponential Models
Section 7-1 I
Exploring Exponential Models
Mrs. Rivas
Ida S. Baker H.S.
You Do It
Identifying Exponential Growth and Decay.
Identify each function as an example of exponential growth or decay. What is the y-intercept? A
𝒚=𝟑 𝟒 𝒙 B
𝒚=𝟏𝟏 𝟎.𝟕𝟓 𝒙
exponential growth.
exponential decay.
y-int. = (𝟎,𝟑)
y-int. = (𝟎,𝟏𝟏) C
You put $2,000 into a college savings account for four years. The account pays 6% interest annually.
exponential growth.
y-int. = (𝟎,𝟐𝟎𝟎𝟎)