Create graphical and algebraic linear models from given data or written descriptions

(i) Copy and complete Table 1 in order to shown how the total charges under package 1 and under the two scenarios for package 2 compare for different amounts of internet access time per month (0, 1 hour and 10 hours)

Table 1
-------------------------------------------------
Access per month/ minutes 0 60 600
--------------------------------------------------
Total cost Package 1 (£) £ 15.99
Total cost package 2 at 3 pence per minute (£)
Total cost package 3 at 5 pence per minute (£)

(ii) Write down three linear equations, one for each of the three schemes listed in Table 1, for the total monthly cost in pounds, y, as a function of access time per month, in minutes, t. Interpret the gradient and y-intercept of these three equations in terms of the different cost for the three schemes.

(iii) Plot graphs of the three functions from part (ii) on your calculator, choosing a window that clearly shows the origin and other points of intersection for the three lines. Sketch the graphs, adding appropriate labeling.

(iv) Use the graphs on your calculator to find the coordinates of the two points at which the lines for package 2 intersect with that for package 1. Find the corresponding access times correct to the nearest minute. Explain briefly how you found them.

(v) Use algebra to find exactly the two different amounts of Internet access time that corresponded to the points where the package 2 scenarios are equivalent in cost to package 1. Explain your working clearly.

(vi)Using your graphs from part (iii) and your answers to parts (iv) 0r (v), find

(a) How long your friend would need to be connected to the Internet each month to ensure that Package 1 was the cheaper option?

(b) The maximum amount of time your friend could be connected to the internet each month to ensure that Package 2 at the 5 pence per minute rate was the cheaper option.