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The number of customers in a grocery store is modeled by the function y -X? + 10x + 50, where y is

the number of customers in the store and x is the number of hours after 7:00 A.M.

a. At what time is the maximum number of customers in the store?

- How many customers are in the store at the time in part (a)?


Sagot :

Using the vertex of the quadratic function, it is found that:

a) The maximum number of customers in the store is at 12 P.M.

b) 75 customers are in the store at this time.

The number of customers in x hours after 7 AM is given by:

[tex]y = -x^2 + 10x + 50[/tex]

Which is a quadratic equation with coefficients [tex]a = -1, b = 10, c = 50[/tex]

Item a:

The maximum value, considering that a < 0, happens at:

[tex]x_v = -\frac{b}{2a}[/tex]

Hence:

[tex]x_v = -\frac{10}{2(-1)} = 5[/tex]

5 hours after 7 A.M, hence, the maximum number of customers in the store is at 12 P.M.

Item b:

The value is y(5), hence:

[tex]y(5) = -(5)^2 + 10(5) + 50 = 75[/tex]

75 customers are in the store at this time.

A similar problem is given at https://brainly.com/question/24713268