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 $$ a $$

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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 $$ a $$.
$$ a $$ can be any real number.

The new value of Stock is modelled by the equation:

Where, .
b. Determine all possible value(s) of

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The new value of Stock is modelled by the equation: Where, . b. Determine all possible value(s) of