Question
The new value of Stock
is modelled by the equation:
Where,
.
b. Determine all possible value(s) of
b. Determine all possible value(s) of
Ask by Rodriguez Hobbs. in Australia
Jan 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
To determine all possible values of
in the equation
, we need to analyze the function and its implications.
-
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. -
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.
- If
-
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:
-
For
: This is already non-negative. -
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: