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.
