# Re: insect word problem

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Posted by T.Gracken on November 10, 2002 at 19:21:17:

In Reply to: insect word problem posted by Sheila on November 10, 2002 at 17:45:25:

: Help, please. I have a word problem concerning insect larvae survival. Soon after they hatch, they must search for food. The survival rate depends on many things and environmental temperature is one of them. For a certain speces of insect, a model of the number of larvae N(T) that survive the searching period is given by N(T) = -0.6T^2 + 32.1T - 350 where T is the temperature in degrees Celsius. I have to answer the following questions:
: a. At what temperature will the maximum number of larvae survive and round my answer to the nearest degree.
: b. What is the maximum number of surviving larvae and round my answer to the nearest whole number.
: c. Find the x-intercepts to the nearest whole number, for the graph of this function.
: d. Write a sentence that describes the meaning of the x-intercept in the context of this problem.

: I am totally clueless as to how to work this in order to answer these questions. Any help would be appreciated.

I can see why you're confused. Whoever wrote the problem is also confused.

But, there is still hope. let's assume the problem writer means "x" is the same as "T". That is, consider the equation:

y = -0.6x2 + 32.1x - 350

[same equation but use x in place of T and y in place of N(T)]

Now, let's look at it from a graph standpoint.

note that it is a parabola that "opens downward". So it has a maximum y-value. And that is the vertex.

So if you remember how to find the vertex, you can answer part (a) by finding the x-value of the vertex.

you can answer part (b) by finding the y-value of the vertex.

you can answer part (c) by substituting 0 in place of y and solving (...use quadratic equation)

you can then answer part (d) by thinking of the results you got for parts a,b, and c.

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