The cost, \(y\) dollars, of printing each T-shirt when \(x\) T-shirts are printed is modelled by the equation \(y=8+\dfrac{400}{x}\), for \(10\leq x\leq160\).
Some corresponding values of x and y are given in the table below.
| \(x\) | \(10\) | \(20\) | \(50\) | \(80\) | \(125\) | \(160\) |
| \(y\) | \(48\) | \(28\) | \(16\) | \(13\) | \(11.2\) | \(p\) |
Find the value of \(p\) in the table above.[1]
On the grid, draw the graph of \(y=8+\dfrac{400}{x}\) for \(10\leq x\leq160\).[2]
Use your graph to estimate the number of T-shirts that is printed if the cost of printing each T-shirt is \$20.[1]
By drawing a tangent, find the gradient of the curve at \((40,18)\).[2]
John suggests that the selling price of each T-shirt, in dollars, is modelled by \(y=30-\dfrac3{16}x\).
On the same grid, draw the graph of \(y=30-\dfrac3{16}x\) for \(0\leq x\leq160\).[1]
Using your graphs, determine the range of values of x for which John will not make any loss, assuming that all of the T-shirts will be sold.[1]