Thank you for visiting Determine whether the equation represents exponential growth exponential decay or neither tex f t 220 1 06 t tex The equation is exponential growth The. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To determine whether the equation represents exponential growth, exponential decay, or neither, and to find the starting value of the function, let's analyze the given function:
The function is given by:
[tex]\[ f(t) = 220(1.06)^t \][/tex]
This is a standard form of an exponential function, where:
- The coefficient [tex]\( 220 \)[/tex] is the starting value or the initial amount.
- The base [tex]\( 1.06 \)[/tex] is the growth or decay factor.
### Step 1: Identify the Starting Value
The starting value is the amount when [tex]\( t = 0 \)[/tex]. In this function:
[tex]\[ f(t) = 220(1.06)^t \][/tex]
When [tex]\( t = 0 \)[/tex]:
[tex]\[ f(0) = 220(1.06)^0 = 220 \times 1 = 220 \][/tex]
Thus, the starting value is [tex]\( 220 \)[/tex].
### Step 2: Determine if the Function Represents Growth or Decay
In an exponential function [tex]\( a(b)^t \)[/tex]:
- If the base [tex]\( b > 1 \)[/tex], the function represents exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
- If [tex]\( b = 1 \)[/tex], the function represents neither growth nor decay.
In our equation:
[tex]\[ b = 1.06 \][/tex]
Since [tex]\( 1.06 > 1 \)[/tex], this means the function represents exponential growth.
### Conclusion
- The equation represents exponential growth.
- The starting value of the function is [tex]\( 220 \)[/tex].
The function is given by:
[tex]\[ f(t) = 220(1.06)^t \][/tex]
This is a standard form of an exponential function, where:
- The coefficient [tex]\( 220 \)[/tex] is the starting value or the initial amount.
- The base [tex]\( 1.06 \)[/tex] is the growth or decay factor.
### Step 1: Identify the Starting Value
The starting value is the amount when [tex]\( t = 0 \)[/tex]. In this function:
[tex]\[ f(t) = 220(1.06)^t \][/tex]
When [tex]\( t = 0 \)[/tex]:
[tex]\[ f(0) = 220(1.06)^0 = 220 \times 1 = 220 \][/tex]
Thus, the starting value is [tex]\( 220 \)[/tex].
### Step 2: Determine if the Function Represents Growth or Decay
In an exponential function [tex]\( a(b)^t \)[/tex]:
- If the base [tex]\( b > 1 \)[/tex], the function represents exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
- If [tex]\( b = 1 \)[/tex], the function represents neither growth nor decay.
In our equation:
[tex]\[ b = 1.06 \][/tex]
Since [tex]\( 1.06 > 1 \)[/tex], this means the function represents exponential growth.
### Conclusion
- The equation represents exponential growth.
- The starting value of the function is [tex]\( 220 \)[/tex].
Thank you for reading the article Determine whether the equation represents exponential growth exponential decay or neither tex f t 220 1 06 t tex The equation is exponential growth The. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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