To determine which models represent compound interest accounts that are growing exponentially, we need to identify which of the given formulas have a base greater than 1. This is because a base greater than 1 signifies exponential growth, while a base less than 1 signifies exponential decay. Let's examine each model step by step:
1. [tex]\( A(t) = 2,675(1.003)^{12t} \)[/tex]
- The base here is [tex]\( 1.003 \)[/tex], which is greater than 1.
- Thus, this model represents exponential growth.
2. [tex]\( A(t) = 4,170(1.04)^t \)[/tex]
- The base here is [tex]\( 1.04 \)[/tex], which is greater than 1.
- Therefore, this model represents exponential growth.
3. [tex]\( A(t) = 3,500(0.997)^{4t} \)[/tex]
- The base here is [tex]\( 0.997 \)[/tex], which is less than 1.
- Hence, this model represents exponential decay.
4. [tex]\( A(t) = 5,750(1.0024)^{2t} \)[/tex]
- The base here is [tex]\( 1.0024 \)[/tex], which is greater than 1.
- Thus, this model represents exponential growth.
5. [tex]\( A(t) = 1,500(0.998)^{12t} \)[/tex]
- The base here is [tex]\( 0.998 \)[/tex], which is less than 1.
- Hence, this model represents exponential decay.
6. [tex]\( A(t) = 2,950(0.999)^t \)[/tex]
- The base here is [tex]\( 0.999 \)[/tex], which is less than 1.
- Therefore, this model represents exponential decay.
Based on the above analysis, the models that represent compound interest accounts growing exponentially are:
- [tex]\( A(t) = 2,675(1.003)^{12t} \)[/tex] (Model 1)
- [tex]\( A(t) = 4,170(1.04)^t \)[/tex] (Model 2)
- [tex]\( A(t) = 5,750(1.0024)^{2t} \)[/tex] (Model 4)
Thus, the correct answers are: [tex]\( \boxed{1, 2, 4} \)[/tex].
