A local taxi association charges a fixed base fare of R12, plus an additional cost per kilometre. A passenger recorded the following amounts paid in a week: Day | Distance travelled (km) | Amount paid (R) | Monday | 5 | 22 | Tuesday | 9 | 30 | Wednesday | 14 | 40 | Thursday | ..... | ..... | Friday | ..... | ..... 1.1 Describe the pattern shown in the taxi fare table in terms of cost, distance, and the pattern that will be formed should a graph be drawn. 1.2 Determine the additional cost per kilometre. Show calculations. 1.3 Write a formula to calculate the taxi fare (C) for any distance travelled (d). 1.4 Use your formula (from Q1.3) to calculate the cost of travelling 43 miles, if 1 km = 0,62 miles.

The problem states a fixed base fare of R12 and an additional cost per kilometre. The table provides data points:

• Monday: 5 km, R22
• Tuesday: 9 km, R30
• Wednesday: 14 km, R40

The pattern shows that the total cost (fare) increases as the distance travelled increases. There is a fixed base fare and an additional cost per kilometre, indicating a linear relationship between cost and distance. If a graph were drawn with distance on the x-axis and cost on the y-axis, it would form a straight line.

We can use any data point from the table and the given base fare of R12.
Using Monday's data:
Total cost = Base fare + (Additional cost per km $\times$ Distance)

Subtract the base fare from the total cost to find the variable cost:

Divide by the distance to find the cost per kilometre:

Using Tuesday's data as a check:

The additional cost per kilometre is consistent.
The additional cost per kilometre is $\boxed{\text{R2/km}}$.

Based on the fixed base fare of R12 and the additional cost of R2 per kilometre:

The formula is $\boxed{C = 12 + 2d}$.

First, convert 43 miles to kilometres using the conversion factor 1 km = 0.62 miles.

Now, use the formula $C = 12 + 2d$ with $d = 69.3548$ km.

Rounding to two decimal places for currency:

The cost of travelling 43 miles is $\boxed{\text{R150.71}}$.