To determine which equations model exponential growth, we need to look for equations of the form \( y = a(b^x) \), where \( a > 0 \) and \( b > 1 \). The base \( b \) must be greater than 1 for the function to represent exponential growth.
Let's analyze the options given:
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\( y = 2( \frac{6}{5})^x \)
- Here, the base is \( \frac{6}{5} \), which is greater than 1. This indicates exponential growth.
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\( y = 3(6)^x \)
- Here, the base is \( 6 \), which is also greater than 1. This indicates exponential growth.
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\( y = 8( \frac{12}{11})^x \)
- Here, the base is \( \frac{12}{11} \), which is greater than 1. This indicates exponential growth.
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\( y = 4( \frac{5}{2})^x \)
- Here, the base is \( \frac{5}{2} \), which is greater than 1. This indicates exponential growth.
All four equations actually represent exponential growth. However, to identify them strictly as exponential growth models based on the conventional form,
- \( y = 2( \frac{6}{5})^x \) (growth)
- \( y = 3(6)^x \) (growth)
- \( y = 8( \frac{12}{11})^x \) (growth)
- \( y = 4( \frac{5}{2})^x \) (growth)
In conclusion, all equations model exponential growth.