Sure. Let's go through this step-by-step.
1. Understand the provided equation:
The straight-line trend equation given is [tex]\( Y = 35 + 2X \)[/tex], where [tex]\( Y \)[/tex] represents the profit in rupees and [tex]\( X \)[/tex] represents the number of years since 2008.
2. Calculate [tex]\( X \)[/tex] for the year 2015:
First, we need to determine the value of [tex]\( X \)[/tex] for the year 2015. Since [tex]\( X \)[/tex] represents the number of years since 2008, we can find [tex]\( X \)[/tex] as follows:
[tex]\[
X = \text{Year} - 2008
\][/tex]
Thus,
[tex]\[
X = 2015 - 2008
\][/tex]
[tex]\[
X = 7
\][/tex]
3. Use the trend equation to estimate the profit:
Now that we have [tex]\( X = 7 \)[/tex], we can substitute this value into the trend equation to estimate the profit for the year 2015:
[tex]\[
Y = 35 + 2X
\][/tex]
Substituting [tex]\( X = 7 \)[/tex]:
[tex]\[
Y = 35 + 2 \cdot 7
\][/tex]
[tex]\[
Y = 35 + 14
\][/tex]
[tex]\[
Y = 49
\][/tex]
4. Conclusion:
The estimated profit for the year 2015 is 49 rupees.
In summary, by applying the given straight line trend equation [tex]\( Y = 35 + 2X \)[/tex], and calculating for [tex]\( X = 7 \)[/tex] (since 2015 is 7 years after 2008), we find that the estimated profit for the year 2015 is 49 rupees.
