Answer:
- **The function starts at 100, and as time increases, the value of \(y\) grows without bound.**
So, the correct option is the one that reflects this behavior.
Explanation:
The given equation is \(y = 100 \times (1.07)^t\), where \(t\) is the time in decades.
Let's analyze the growth:
- The base of the exponent, \(1.07\), is greater than 1, indicating exponential growth.
- Since the base is greater than 1, the function will increase without bound as \(t\) increases.
Now, to address the options:
1. If \(t = 0\), \(y = 100 \times (1.07)^0 = 100\). This means that initially, the value is 100.
2. If \(t\) is positive, the exponent will be positive, leading to exponential growth. The larger the value of \(t\), the larger the result.
Based on this analysis, the statement that is true is:
- The function starts at 100, and as time increases, the value of \(y\) grows without bound.
So, the correct option is the one that reflects this behavior.