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Answer :
Final answer:
To find the number of cars sold in the fourth week, use the given data points to find the equation of the line using the slope formula and point-slope form of a linear equation. Substitute x = 4 into the equation to find the number of cars sold.
Explanation:
To find the number of cars sold in the fourth week, we need to determine the pattern or trend of car sales. The problem states that the number of cars sold grows according to a linear growth model. We can use the given data points to find the equation of the line and then plug in the value for the fourth week to find the number of cars sold.
First, we need to find the slope (m) of the line using the formula:
m = (P1 - P0) / (1 - 0)
where P1 is the number of cars sold in the second week (12) and P0 is the number of cars sold in the first week (5).
Using this formula, we find that m = (12 - 5) / (1 - 0) = 7. So, the slope of the line is 7.
Next, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is the point (1, 5) and m is the slope (7).
Plugging in these values, we have:
y - 5 = 7(x - 1)
Simplifying the equation, we get:
y - 5 = 7x - 7
y = 7x - 2
Now we can substitute x = 4 into the equation to find y:
y = 7(4) - 2
y = 28 - 2
y = 26
Therefore, the dealership is expected to sell 26 cars in the fourth week.
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