1. First we are going to find the cost function.
We know for our problem that there is a 7% sales tax applied to the cost of her meal and she plans to leave 3$ as tip. Let
represent the cost of the meal:
where
is the cost of the entree
is the total cost she will pay
We know that the minimum cost of an entree is $5.98, so the domain of our functions so far is:
Now, to find the upper limit of the domain, we are going to take advantage of the fact the she only has $15 to spend, so we can replace the total cost with 15 and solve for:
We can conclude that the domain of the function is
2. We know that Mia's friend Clara loans her $5, so Mia's total money now is $15+$5=$20. Since the minimum cost for an entree remains the same ($5.98), the lower limit of our domain remains the same:
Now, to find the upper limit of our domain, we are going to replace the total cost with 20 an solve for:
We can conclude that the domain of the function representing the price of an entree Mia can afford is now
We know for our problem that there is a 7% sales tax applied to the cost of her meal and she plans to leave 3$ as tip. Let
where
We know that the minimum cost of an entree is $5.98, so the domain of our functions so far is:
Now, to find the upper limit of the domain, we are going to take advantage of the fact the she only has $15 to spend, so we can replace the total cost with 15 and solve for
We can conclude that the domain of the function is
2. We know that Mia's friend Clara loans her $5, so Mia's total money now is $15+$5=$20. Since the minimum cost for an entree remains the same ($5.98), the lower limit of our domain remains the same:
Now, to find the upper limit of our domain, we are going to replace the total cost with 20 an solve for
We can conclude that the domain of the function representing the price of an entree Mia can afford is now