the function g models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function…
the function g models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function of rainfall (in centimeters) in that area. which of these statements are true? choose all answers that apply: a more rainfall relates to more mosquitoes as long as rainfall is less than 2 cm. b more rainfall relates to more mosquitoes as long as rainfall is more than 2 cm. c when there is no rainfall, there are about 1 million mosquitoes. d when there is no rainfall, there are about 2 million mosquitoes.
Answer
Explanation:
Step1: Analyze the function's trend
The function (g) is a parabola opening downwards. For a parabola (y = ax^{2}+bx + c) ((a<0)), the function is increasing on the left - hand side of the vertex and decreasing on the right - hand side of the vertex. The vertex of the parabola (in the context of this problem) occurs at (x = 2) (where (x) represents rainfall in centimeters). When (x<2), as (x) (rainfall) increases, (y = g(x)) (number of mosquitoes) increases. When (x>2), as (x) (rainfall) increases, (y = g(x)) (number of mosquitoes) decreases.
Step2: Analyze the (y) - intercept
The (y) - intercept of the function (y = g(x)) is the value of (y) when (x = 0) (no rainfall). Looking at the graph, when (x = 0), (y=0)
Answer:
A. More rainfall relates to more mosquitoes as long as rainfall is less than 2 cm.