The new value of Stock \( S \) is modelled by the equation: \[ s_{2}:[0, \infty) \rightarrow \mathbb{R}, s_{2}(t)=a t+3 \] Where, \( a \in \mathbb{R} \). b. Determine all possible value(s) of \( a \)

To determine all possible values of \( a \) in the equation \( s_{2}(t) = a t + 3 \), we need to analyze the function and its implications. 1. **Understanding the function**: The function \( s_{2}(t) \) is a linear function of \( t \) with a slope of \( a \) and a y-intercept of 3. The domain of \( t \) is from 0 to infinity, which means we are interested in the behavior of the stock value as time progresses. 2. **Behavior of the function**: - If \( a > 0 \): The stock value \( s_{2}(t) \) will increase as \( t \) increases, indicating a positive growth in stock value over time. - If \( a = 0 \): The stock value \( s_{2}(t) \) will remain constant at 3, meaning there is no growth or decline. - If \( a < 0 \): The stock value \( s_{2}(t) \) will decrease as \( t \) increases, indicating a decline in stock value over time. 3. **Possible values of \( a \)**: Since \( a \) can take any real number value, the possible values of \( a \) are: \[ a \in \mathbb{R} \] Thus, the conclusion is that \( a \) can be any real number, which means there are no restrictions on the value of \( a \).