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

Ask by Rodriguez Hobbs. in Australia
Jan 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

can be any real number.

Solution

To determine all possible values of in the equation , we need to analyze the function and its implications.
  1. Understanding the function: The function is a linear function of with a slope of and a y-intercept of 3. The domain of 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 : The stock value will increase as increases, indicating a positive growth in stock value over time.
    • If : The stock value will remain constant at 3, meaning there is no growth or decline.
    • If : The stock value will decrease as increases, indicating a decline in stock value over time.
  3. Possible values of : Since can take any real number value, the possible values of are:
Thus, the conclusion is that can be any real number, which means there are no restrictions on the value of .

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Bonus Knowledge

To ensure that the function represents a valid stock value, we must take into consideration that stock prices are generally non-negative. This implies:
  1. For :
    This is already non-negative.
  2. For :
    We have . For this to remain non-negative for all , the slope must be such that .
If , as increases, would become more negative, and there will be a point where . This scenario violates the condition of non-negativity. Thus, must be non-negative.
Therefore, the possible value(s) of are:

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