The function C(x) = x 2 + 78 x + 29 models the cost, in hundreds of dollars, to produce x thousand pens. Find and interpret C(0), C(2) and C(4)

Answer:

Step-by-step explanation:

Given the function C(x) = x 2 + 78 x + 29 models the cost, in hundreds of dollars, to produce x thousand pens, we are to interpret C(0), C(2) and C(4).

For C(0), we are to substitute x = 0 into the given function;

C(0) = 0²+78(0)+29

C(0) = 0+0+29

C(0) = 29

Since the cost C(x) is in hundreds of dollars, C(0) = 2900

C(0) means that the cost of producing 0 thousand pen is $2,900

For C(2), we are to substitute x = 2 into the given function;

C(2) = 2²+78(2)+29

C(2) = 4+156+29

C(2) = 189

Since the cost C(x) is in hundreds of dollars, C(2) = 189*100 = $18900

C(2) means that the cost of producing 2 thousand pens is $18,900

For C(4), we are to substitute x = 4 into the given function;

C(4) = 4²+78(4)+29

C(4) = 16+312+29

C(4) = 357

Since the cost C(4) is in hundreds of dollars, C(4) = 357

C(4) means that the cost of producing 4 thousand pens is $35,700

Final answer:

C(x) = x^2 + 78x + 29 models the cost to produce x thousand pens. Calculating C(0), C(2), and C(4), we find that C(0) = 29, C(2) = 189, and C(4) = 357. These values represent the cost in hundreds of dollars for producing 0, 2, and 4 thousand pens, respectively.

Explanation:

To find and interpret C(0), C(2), and C(4), we substitute the given values of x into the function C(x).

1.For C(0), we substitute 0 into the function C(x):

1. C(0) = (0)^2 + 78(0) + 29
2. C(0) = 0 + 0 + 29
3. C(0) = 29
4. So, C(0) = 29 hundred dollars, meaning it costs $2900 to produce 0 thousand pens.
5. For C(2), we substitute 2 into the function C(x):
6. C(2) = (2)^2 + 78(2) + 29
7. C(2) = 4 + 156 + 29
8. C(2) = 189
9. So, C(2) = 189 hundred dollars, meaning it costs $18,900 to
10. produce
11. 2 thousand pens.
12. For C(4), we substitute 4 into the function C(x):
13. C(4) = (4)^2 + 78(4) + 29
14. C(4) = 16 + 312 + 29
15. C(4) = 357
16. So, C(4) = 357 hundred dollars, meaning it costs $35,700 to produce 4 thousand pens.

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