Taxicab fees A taxicab ride costs $3.50 plus ...

Question

Taxicab fees A taxicab ride costs $3.50 plus $2.50 per mile. Let m be the distance (in miles) from the airport to a hotel. Find and graph the function c(m) that represents the cost of taking a taxi from the airport to the hotel. Also determine how much it will cost if the hotel is 9 miles from the airport.

Accepted Answer

Welcome back. Everyone in this problem. A water park charges $5 as entry fees and charges $1.50 for each hour. A person stays in the water park determine the cost function C of T if a person stays for two hours in the water park, draw the graph of the function and find the cost charged by the water park management for six hours here for our answer choices. A says that the cost function is 1.5 T plus five and the cost charged by management for six hours is $14. B says the function is 1.5 T minus five and C of six equals $4. C says C of T equals 1.5 T plus five and C of six is $14. And D says C of T equals 1.5 T minus five and C of six is $4. Now, if we're going to figure out, ok, uh what our cost function is and our graph and the cost charged by the water park management. Let's take a closer look at our problem statement. Now, recall, ok, that the linear function, ok. In this case CFT is of the form MT plus B, OK? Where M represents the slope and B represents the Y intercept. Now, first, if we're thinking about the slope, OK, if our graph is of T versus C of T, OK, then our slope is going to be our change in hours per hour or a charge per hour. And in our problem, we are told that our wat water park charges one point sorry, $1.50 for each hour, a person stays in the water park. So already this tells us that m the charge per hour equals 1.5. And we're told that our water park charges $5 as entry fees. Ok. And we know, let me just fix that here since that's a fixed cost, a fixed charge that represents our Y intercept B which is five. Therefore, that tells us then that our cost function C of T is going to be equal to 1.5 T plus five. Ok. Now, or are we going to draw the graph of the function? Well, since it's a linear function, OK, then we only need two points to plot our graph. So let's figure out those two points. Let's start with when T equals zero. When T equals zero, then C of zero is going to be equal to 1.5 times zero plus five, which would be equal to five. So 05 is a point on the graph. Next, when T equals two C of two equals 1.5 multiplied by two, which is three plus five, which equals eight. So that tells us that 28 is also on our graph. So whatever graph we're going to find, I mean, we already have our graphs plotted in our, in our answers. But whatever the graph is then we know that it's going to have the points 05. OK? And 28 on the graph. So our graph is gonna probably look something like this. OK. So we can look for a graph in this direction with those two points. Now, finally, we want to find the cost charged by the water park management for six hours. Now let me just correct something on our graph here. OK. My apologies. But we know that our graph is going to start at zero. OK. Start at T equals zero because we can't have a negative time. OK? So rather a sketch is going to look something like this or, or a graph now for six hours. OK? For T equals six. OK. Then our cost is going to be equal to 1.5 multiplied by six plus five, 1.5 multiplied by six equals nine and nine plus five equals 14. So in other words, the cost after six hours would be $14. Let's look at our answer choices, which one of them has the cost function as 1.5 T plus five. A graph that looks like this and C six equal to $14 here. We can see that A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Linear Functions

Graphing Functions

Evaluating Functions

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