In a certain forest, the leaf density can be modeled by the equation
y = 20 + 15 sin(pi/6 (t-3)) where y represents the number of leaves per square foot and t represents the number of months after January
a. What is the period of this function and what does the period represent?
b. What is the maximum leaf density that occurs in this forest and when does this occur?
Algebra 2?
2015-08-31 8:33 pm
回答 (1)
2015-08-31 9:22 pm
✔ 最佳答案
a. (2π)/(π/6) = 12. The period of the function is 12 months. The period always represents the length of time between maxima (or minima). It represents the length of one complete cycle of the function.b. (π/6)(t-3) = π/2
.. t-3 = 3
.. t = 6 ... Maximum leaf density is 35 leaves/ft^2. This occurs 6 months after January, in July.
(The maximum value of sin( ) is 1, so y = 20+15 = 35 is the maximum value of y.)
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