a) What is always the same?
The initial charge for the taxi service is always the same, which is $3 for the first mile.
b) What changes with each mile driven?
The amount charged for each additional mile changes with each mile driven. It is $0.20 for each additional mile beyond the first mile.
c) Write an equation, p, for how much a person has to pay after being driven m miles.
The equation for the cost of a taxi ride after being driven m miles can be expressed as:
p(m) = 3 + 0.20(m - 1)
In this equation, 3 represents the initial charge for the first mile, and 0.20(m - 1) represents the additional charge for each mile beyond the first.
d) If a person knows that they paid $4.40 for the trip, write a function they can use to figure out how many miles they went.
To figure out the number of miles driven when the cost is $4.40, you can rearrange the equation from part c:
4.40 = 3 + 0.20(m - 1)
Now, solve for m:
0.20(m - 1) = 4.40 - 3
0.20(m - 1) = 1.40
m - 1 = 1.40 / 0.20
m - 1 = 7
m = 7 + 1
m = 8 miles
e) Calculate the number of miles in part d.
The person traveled 8 miles for a total cost of $4.40.
f) Now that you know how many miles were traveled, how can you use your equation from part c to check if you were correct?
You can use the equation p(m) = 3 + 0.20(m - 1) with m = 8 to check if the cost matches. Plug in m = 8:
p(8) = 3 + 0.20(8 - 1)
p(8) = 3 + 0.20(7)
p(8) = 3 + 1.40
p(8) = 4.40
The cost calculated using the equation matches the actual cost, which is $4.40. So, the answer is correct.