Identifying The Characteristics of Linear and Exponential Functions
Function	Type and Behavior
d(y)=6(4)y	Select an answer Exponential Linear  Select an answer Increasing Decreasing 
p(t)=60(1.2)t	Select an answer Exponential Linear  Select an answer Increasing Decreasing 
g(x)=-14x+130	Select an answer Exponential Linear  Select an answer Increasing Decreasing 
h(x)=220(0.9)x	Select an answer Exponential Linear  Select an answer Increasing Decreasing 
f(x)=28x-50	Select an answer Exponential Linear  Select an answer Increasing Decreasing 


Let's analyze the given functions one by one to identify their type (linear or exponential) and behavior (increasing or decreasing):

1. **\( d(y) = 6(4)^y \)**  
   - **Type**: This is an exponential function because the variable \( y \) is in the exponent.  
   - **Behavior**: Since the base \( 4 > 1 \), the function is increasing.  
   **Answer**: Exponential, Increasing.

2. **\( p(t) = 60(1.2)^t \)**  
   - **Type**: This is an exponential function because the variable \( t \) is in the exponent.  
   - **Behavior**: Since the base \( 1.2 > 1 \), the function is increasing.  
   **Answer**: Exponential, Increasing.

3. **\( g(x) = -14x + 130 \)**  
   - **Type**: This is a linear function because the variable \( x \) is to the first power, and there is no exponent.  
   - **Behavior**: The slope is \( -14 \), which is negative, so the function is decreasing.  
   **Answer**: Linear, Decreasing.

4. **\( h(x) = 220(0.9)^x \)**  
   - **Type**: This is an exponential function because the variable \( x \) is in the exponent.  
   - **Behavior**: Since the base \( 0.9 < 1 \), the function is decreasing.  
   **Answer**: Exponential, Decreasing.

5. **\( f(x) = 28x - 50 \)**  
   - **Type**: This is a linear function because the variable \( x \) is to the first power, and there is no exponent.  
   - **Behavior**: The slope is \( 28 \), which is positive, so the function is increasing.  
   **Answer**: Linear, Increasing.

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Do you want more details on how to analyze such functions? 

Here are 5 related questions that might interest you:
1. What makes a function linear or exponential?
2. How do you determine if an exponential function is increasing or decreasing?
3. Can a linear function have a curve?
4. What real-world phenomena can be modeled by exponential functions?
5. How do you find the slope of a linear function?

**Tip**: In exponential functions, the base determines growth or decay—if the base is greater than 1, the function grows (increases); if the base is between 0 and 1, it decays (decreases).

Identifying The Characteristics of Linear and Exponential Functions
Function	Type and Behavior
d(y)=6(4)^y	Select an answer Exponential Linear	Select an answer Increasing Decreasing
p(t)=60(1.2)^t	Select an answer Exponential Linear	Select an answer Increasing Decreasing
g(x)=-14x+130	Select an answer Exponential Linear	Select an answer Increasing Decreasing
h(x)=220(0.9)^x	Select an answer Exponential Linear	Select an answer Increasing Decreasing
f(x)=28x-50	Select an answer Exponential Linear	Select an answer Increasing Decreasing

Explore the characteristics of linear and exponential functions, including key formulas and behavior analysis (increasing or decreasing). This problem involves functions such as d(y) = 6(4)^y, p(t) = 60(1.2)^t, and others. Suitable for Grades 9-11.

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