Question 281319: The problem given in the book is:
1.) For certain species of insect, a model of the number of larvae, N(T), that survive during this period is given by
N(T)= -0.6T^2 + 32.1T - 350
[T is the temperature in degrees celsius]
a.) At what temperature will the maximum number of larvae survive? Round to the nearest degree. [I understand that this involves a parabola, however, the graph given by my calculator states "error" each time I attempt to "plug in" the problem.]
b.) What is the maximum number of surviving larvae? Round to the nearest whole number
c.) find the x-intercepts, to the nearest whole number, for the graph of this function. [I assume this means making a "T-chart," though the function on my calculator can't work if I am unable to properly insert the equation in my calculator.]
d.) Write a sentence that describes the meaning of the x-intercepts in the context of this problem.
[I've also reached the assumption that this correlates with the idea of inputs and outputs. So with each x-intercept input, the y-intercept output will correspond according to the parabola.]
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 1.) For certain species of insect, a model of the number of larvae, N(T), that survive during this period is given by
N(T)= -0.6T^2 + 32.1T - 350
[T is the temperature in degrees celsius]
a.) At what temperature will the maximum number of larvae survive? Round to the nearest degree.
Yes, this is a parabola.
Since the coefficient associated with the T^2 term is NEGATIVE, we know that the parabola opens downward. Thus if we find the "axis of symmetry" it will give us the max temperature. Axis of symmetry is found by:
x = -b/(2a)
x = -32.1/(2(-0.6))
x = -32.1/(-1.2)
x = 26.75 celsius
.
b.) What is the maximum number of surviving larvae? Round to the nearest whole number
Since N(T) gives us the number as a function of temperature we simply plug in the value found above into:
N(T)= -0.6T^2 + 32.1T - 350
N(26.75)= -0.6(26.75^2) + 32.1(26.75) - 350
N(26.75)= 79
.
c.) find the x-intercepts, to the nearest whole number, for the graph of this function.
To find the x-intercepts, set N(T) to zero and solve for T:
N(T)= -0.6T^2 + 32.1T - 350
0 = -0.6T^2 + 32.1T - 350
Using the quadratic equation gives you:
T = {15.25, 38.25}
.
d.) Write a sentence that describes the meaning of the x-intercepts in the context of this problem.
These are the temperatures where no larvae will be produced -- optimum temperatures to rid yourself of this type of insects.
|
|
|
