The height of a plant, y , in centimeters, is measured x weeks after planting a seed. The height can be modeled by the regression equation y is equal to the fraction with numerator 6 point 8 8 and denominator 1 plus 2 comma 139 point 9 9 e raised to the negative 0 point 4 7 x power Which statement best interprets the value 6 point 8 8 ?
Answer
A
The plant grows 6 point 8 8 centimeters each week.
B
The plant takes 6 point 8 8 weeks to reach a height of 2 comma 139 point 9 9 centimeters .
C
The limiting value for the height of the plant is 6 point 8 8 centimeters .
D
The initial height of the plant is 6 point 8 8 centimeters .
Explanation
As x increases, e^(-0.47x) approaches 0, so the denominator approaches 1. Therefore, y approaches 6.88 centimeters. This means 6.88 centimeters is the limiting height of the plant, not its initial height or weekly growth.
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