A proposed train fare would charge 20 pesos for the first five kilometers if travel and 0.75 for each additional kilometer over the proposed fare. Find the fare function f(x) where x represents the number of kilometers traveled
Oh, I see! So you're looking for a mathematical representation for the fare function. Let's break it down, shall we?
We know that the fare for the first five kilometers is a fixed amount of 20 pesos. After that, for each additional kilometer, it's 0.75 pesos.
So, if we express this in a mathematical form, the fare function f(x) can be defined as:
f(x) = 20 + 0.75(x - 5)
Let me explain. (x - 5) represents the number of additional kilometers beyond the initial five kilometers, and we multiply it by 0.75 because that's the rate per additional kilometer. Finally, we add 20 to account for the fixed fare for the first five kilometers.
Now, go enjoy your train ride, and remember to let me know if you have any more "fare"-minded questions!
To find the fare function, we need to determine how the fare changes based on the number of kilometers traveled.
According to the given information, the fare for the first five kilometers is a fixed amount of 20 pesos. After that, for each additional kilometer, the fare increases by 0.75 pesos.
Let's break down the fare calculation based on the number of kilometers traveled:
- For the first five kilometers (0 <= x <= 5), the fare is 20 pesos.
- For each additional kilometer (x > 5), the fare increases by 0.75 pesos.
To represent this in a mathematical function, we can define the fare function as follows:
f(x) = 20 + 0.75(x - 5)
Let's understand how this function works:
- If x <= 5 (traveling within or up to 5 kilometers), the value of (x - 5) will be negative or zero, resulting in an additional fare of zero pesos. Therefore, the fare will remain constant at 20 pesos.
- If x > 5 (traveling beyond 5 kilometers), (x - 5) will be a positive value, representing the additional kilometers beyond the initial five kilometers. We multiply this value by 0.75 pesos to calculate the additional fare and add it to the fixed fare of 20 pesos.
For example, let's calculate the fare for various distances using the fare function f(x):
- For x = 3 kilometers:
f(3) = 20 + 0.75(3 - 5) = 20 + 0.75(-2) = 20 - 1.5 = 18.5 pesos
- For x = 6 kilometers:
f(6) = 20 + 0.75(6 - 5) = 20 + 0.75(1) = 20 + 0.75 = 20.75 pesos
- For x = 10 kilometers:
f(10) = 20 + 0.75(10 - 5) = 20 + 0.75(5) = 20 + 3.75 = 23.75 pesos
So, the fare function f(x) = 20 + 0.75(x - 5) represents the fare in pesos based on the number of kilometers traveled.