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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