We appreciate your visit to From the following exponential mathematical model list the growth or decay constant that represents the growth or decay rate Also state whether it is a. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine the growth or decay constant in the given exponential model and identify if it's related to growth or decay, let's look at the model:
[tex]\[ A = 173 e^{0.008 t} \][/tex]
1. Identify the Exponential Part: In this expression, the exponential part is [tex]\( e^{0.008 t} \)[/tex].
2. Locate the Constant: The constant in the exponent, which is multiplied by [tex]\( t \)[/tex], is [tex]\( 0.008 \)[/tex].
3. Determine the Type (Growth or Decay):
- If the constant in the exponent (0.008 in this case) is positive, it indicates a growth process. This is because as [tex]\( t \)[/tex] (time) increases, the value of [tex]\( e^{0.008 t} \)[/tex] also increases.
- Conversely, if the constant were negative, it would imply decay, as the expression would decrease over time.
In this model, since the constant [tex]\( 0.008 \)[/tex] is positive, it is indeed a growth constant. Therefore, the correct answer is:
- The growth constant is [tex]\( 0.008 \)[/tex], and it represents a growth rate.
[tex]\[ A = 173 e^{0.008 t} \][/tex]
1. Identify the Exponential Part: In this expression, the exponential part is [tex]\( e^{0.008 t} \)[/tex].
2. Locate the Constant: The constant in the exponent, which is multiplied by [tex]\( t \)[/tex], is [tex]\( 0.008 \)[/tex].
3. Determine the Type (Growth or Decay):
- If the constant in the exponent (0.008 in this case) is positive, it indicates a growth process. This is because as [tex]\( t \)[/tex] (time) increases, the value of [tex]\( e^{0.008 t} \)[/tex] also increases.
- Conversely, if the constant were negative, it would imply decay, as the expression would decrease over time.
In this model, since the constant [tex]\( 0.008 \)[/tex] is positive, it is indeed a growth constant. Therefore, the correct answer is:
- The growth constant is [tex]\( 0.008 \)[/tex], and it represents a growth rate.
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