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A freight train traveling along a certain route uses 12 units of fuel per mile plus an additional 2.2 units of fuel per mile for each railcar on the train. Let N represent the number of railcars on the train. What is an expression for f(N), the total number of units of fuel used per mile? find f(12). How many railcars does the train have if f(N)=34?

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Answer:

[tex]38.4\ \text{units of fuel/mile}[/tex]

10

Step-by-step explanation:

Let [tex]N[/tex] represent the number of rail cars on the train

Each rail car adds 2.2 units of fuel per mile.

Fixed fuel consumption is 12 units of fuel per mile

The function of fuel consumption per mile is

[tex]f(N)=12+2.2 N[/tex]

when

[tex]N=12[/tex]

[tex]f(12)=12+2.2\times 12\\\Rightarrow f(12)=38.4\ \text{units/mile}[/tex]

[tex]\boldsymbol{f(12)=38.4\ \text{units/mile}}[/tex]

[tex]f(N)=34\\\Rightarrow 12+2.2N=34\\\Rightarrow N=\dfrac{34-12}{2.2}\\\Rightarrow N=10[/tex]

So, the number of rail cars when [tex]f(N)=34[/tex] is 10.

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