Q:

Imagine that you have an elementary school-age child and are researching childcare options. You find two that you like – one at a child-care center, one is based in a family's home – so it basically comes down to which one will be cheapest. The child-care center charges $300 to enroll, then $79 per week. The family-run childcare charges $180 to enroll, then $93 per week.a. Setup two functions to represent the cost of each. b. Which childcare approach will be the cheapest in the short-term, child-care center or family-run? c. To choose which plan is best, you need some idea of how long your child will be enrolled. Determine the number of weeks at which it becomes more cost-effective to choose the long-term option.

Accepted Solution

A:
Answer:a) Cost of the child-care center: y = 300 + 79xCost of the family-run childcare: y = 180 + 93xWhere x is the number of weeks.b) Β In the short-term, the family-run childcare will be cheapest because the charge for enrolling is less than for the child-care center.c)The long term option (child-care center) becomes more cost-effective if you plan to enroll your child for more than 8.6 weeks. Step-by-step explanation:Hi there!a)Let y be the cost of childcare. In the child-care center, the cost is 300 plus 79 per week. Let x be the number of weeks, then the cost function for the child-care center will be:y = 300 + 79xIn the same way, the cost of the family-run childcare will be:y = 180 + 93xb) In the short-term, the family-run childcare will be cheapest because the charge for enrolling is less than for the child-care center. LetΒ΄s calculate the cost of both childcare options for low values of x:Child-care center:y = 300 + 79 xx = 0, y = 300x = 1, y = 379x = 2, y = 458x = 3, y = 537x = 4, y = 616Family-run:y = 180 + 93xx = 0, y = 180x = 1, y = 273x = 2, y = 366x = 3, y = 459x = 4, y = 552c) We have to find the value of x for which the cost of the family-run childcare is greater than the cost of the child-care center:cost family-run > child-care center180 + 93x > 300 + 79 x93x -79x >300 - 18014x > 120x > 120/14x > 8.6The long term option (child-care center) becomes more cost-effective if you plan to enroll your child for more than 8.6 weeks.