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o-na [289]
3 years ago
9

The Candy Factory sells candy by the pound, charging $1.60 per pound for quantities up to and including 20 pounds. Above 20 poun

ds, the Candy Factory charges $1.30 per pound for the entire quantity, plus a quantity surcharge k. If x represents the number of pounds, the price function is p(x) = {1.60x for x lessthanorequalto 20, 1.30x + k for x > 20. Find k such that the price function p is continuous at x =20. Explain why it is preferable to have continuity at x =20. The price function p is continuous at x = 20 when k = (Type an integer or a decimal.)
Mathematics
1 answer:
rusak2 [61]3 years ago
5 0

Answer:

k=6

Step-by-step explanation:

We have been given that the Candy Factory sells candy by the pound, charging $1.60 per pound for quantities up to and including 20 pounds. Above 20 pounds, the Candy Factory charges $1.30 per pound for the entire quantity, plus a quantity surcharge k.

\left \{ {{p(x)=1.6x, \text{ If }x\leq 20} \atop {p(x)=1.30x+x,\text{ if }x>20}} \right.

For the price function be to continuous at x=20, the value of both functions at x=20 must be equal. Because a function is continuous if the right hand limit is equal to left hand limit.

1.6(20)=1.3(20)+k

Let us solve for k.

32=26+k

32-26=26-26+k\\\\6=k

Therefore, the price function p is continuous at  x=20, when k is equal to 6.

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