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the fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees celsius) is modeled by:
P(x)=-2(x-9)^2+200
what temperature will result in the maximum number of fish?

the fish population in a certain part of the ocean in thousands of fish as a function of the waters temperature in degrees celsius is modeled by Px2x92200 what class=

Respuesta :

  • y=-2(x-9)²+200

Compare to vertex form of parabola y=a(x-h)²+k

Vertex:-

  • (h,k)=(9,200)

As a is negative vertex is maximum

Max temperature=9°C

semsee45

Answer:

9 °C

Step-by-step explanation:

Given function:

[tex]P(x)=-2(x-9)^2+200[/tex]

The given function is a quadratic in vertex form.

Vertex form:  [tex]y=a(x-h)^2+k[/tex]  (where (h, k) is the vertex)

Therefore, the vertex is (9, 200)

The vertex is the minimum point for a parabola that opens upward.

The vertex is the maximum point for a parabola that opens downward.

The given function has a negative leading coefficient, therefore is opens downwards, and the vertex is the maximum point.

Therefore, the temperature (x-value) that will give the maximum number of fish (y-value) is the x-value of the vertex:  9 °C

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