Question

A taxi charges a base fee plus $0.75/km.

Answer 1

Answer:

a)  $0.75/Km

b) $F(x)=1.2+0.75x$

c) The fixed base charge

Step-by-step explanation:

We know the taxi charges $0.75 per km and we are told a 10-Km trip costs $8.70. We can clearly see there is a base charge and a variable charge

a) The rate of change tells us the variation of the charges with the distance of the trip. In this case, the rate of change is $0.75/Km

b) If x is the length of the trip in Km, the equation of the total fare F(x) is

$F(x)=A+0.75x$

We know a 10-Km trip costs $8.70. Replacing those values would give us the value of A

8.70=A+0.75(10)

8.70=A+7.5

$=> A=8.70-7.5= 1.2$

Using the value of A we have

$\boxed{F(x)=1.2+0.75x}$

c) The initial value represents the charge a customer has to pay even if they don't travel any distance, i.e. the fixed base charge

Answer 2

a) The rate of change in this situation is 0.75 dollars/km

b) The equation for the cost of hiring a taxi in terms of length of the

trip is y = 0.75 x + b

c) The initial value represents in this situation is $1.2

Step-by-step explanation:

The given is:

• A taxi charges a base fee plus $0.75/km.
• A 10-km trip costs $8.70

∵ A rate of change is a rate that describes how one quantity

  changes in relation to another quantity

∵ The unit cost of a taxi is 0.75 dollars for each 1 kilometer

∴ The rate of change = 0.75 dollars/km

a) The rate of change in this situation is 0.75 dollars/km

Assume that the cost of hiring a taxi is $y for length of a trip x km

and a base fee of $b

∵ The length of the trip = x km

∵ The cost per km = $0.75

∵ The base fee = $b

∵ The cost of hiring a taxi = $y

- Write an equation for the the cost of hiring a taxi

∴ y = 0.75 x + b

b) The equation for the cost of hiring a taxi in terms of length

of the trip is y = 0.75 x + b

∵ The length of the trip is 10 km

∴ x = 10

∵ The cost of the hiring a taxi is $8.70

∴ y = 8.70

- Substitute these values in the equation of part (b)

∵ y = 0.75 x + b

∴ 8.70 = 0.75(10) + b

∴ 8.70 = 7.5 + b

- Subtract 7.5 from both sides

∴ 1.2 = b

∵ b is the base fee

∴ b is the initial value

∴ The initial value = $1.2

c) The initial value represents in this situation is $1.2

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