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A company uses functions to model the costs to produce and market a product.

The cost, in thousands of dollars, to produce [tex]\(x\)[/tex] units of the product is modeled by function [tex]\(f\)[/tex]: [tex]\(f(x) = 17 + 0.05x\)[/tex].

The cost, in thousands of dollars, to market [tex]\(x\)[/tex] units of the product is modeled by function [tex]\(k\)[/tex]: [tex]\(k(x) = 4 + 0.03x\)[/tex].

Which function correctly represents the total cost, in thousands of dollars, to produce and market [tex]\(x\)[/tex] units of the product?

A. [tex]\(c(x) = 21 + 0.08x\)[/tex]

B. [tex]\(c(x) = 21 + 0.08x^2\)[/tex]

C. [tex]\(c(x) = 13 + 0.02x\)[/tex]

D. [tex]\(c(x) = 13 + 0.02x^2\)[/tex]



Answer :

GinnyAnswer
To determine the function that correctly represents the total cost to produce and market [tex]\(x\)[/tex] units of the product, we need to add the individual costs given by the functions [tex]\(f(x)\)[/tex] and [tex]\(k(x)\)[/tex].

The function for the cost to produce [tex]\(x\)[/tex] units is:
[tex]\[ f(x) = 17 + 0.05x \][/tex]

The function for the cost to market [tex]\(x\)[/tex] units is:
[tex]\[ k(x) = 4 + 0.03x \][/tex]

To find the total cost to produce and market [tex]\(x\)[/tex] units, we sum these two functions:
[tex]\[ c(x) = f(x) + k(x) \][/tex]

Now we substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(k(x)\)[/tex]:
[tex]\[ c(x) = (17 + 0.05x) + (4 + 0.03x) \][/tex]

Next, we combine the constant terms and the terms involving [tex]\(x\)[/tex]:
[tex]\[ c(x) = 17 + 4 + 0.05x + 0.03x \][/tex]

Simplify the constants and combine the [tex]\(x\)[/tex]-terms:
[tex]\[ c(x) = 21 + 0.08x \][/tex]

Therefore, the function that correctly represents the total cost to produce and market [tex]\(x\)[/tex] units of the product is:
[tex]\[ \boxed{c(x) = 21 + 0.08x} \][/tex]

Thus, the correct answer is:
A. [tex]\(c(x) = 21 + 0.08x\)[/tex]

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