Question

p(x)={(1.40x for x<=30),(1.10x+k for x>30):} Find k such that the price function p is continuous at x=30.

Answer 1

To make the price function p continuous at x = 30, the value of k should be 9.

Step-by-step explanation:

To find k such that the price function p is continuous at x = 30, we need to make sure that the value of p(x) at x=30 from both sides of the equation is the same.

For x<=30, p(x) = 1.40x. So, p(30) = 1.40(30).

For x>30, p(x) = 1.10x+k. So, p(30) = 1.10(30)+k.

Setting these two equal to each other, we have: 1.40(30) = 1.10(30) + k. Solving for k, we get k = 1.40(30) - 1.10(30) = 42 - 33 = 9.

Therefore, k = 9.