I had to baby-talk mny way through it . . .Prospectors are drilling for oil.
The cost of drilling to a depth of 50m is $500.
To drill a further 50m costs $640
and, hence, the total cost of drilling to a depth of 100m is $1140.
Each subsequent extra depth of 50m costs $140 more to drill than the previous 50m.
The total sum of money available for drilling is $76,000.
Find, to the nearest 50m, the greatest depth that can be drilled.
We have a Cost sequence: .
Take the difference of consecutive terms,
. . then take differences of the differences, etc.
The second differences are constant.
. . Hence, the function is of the second degree . . . a quadratic.
The general quadratic function is: .
Plug in the first three values of the sequence:
We have: .
Quadratic Formula: .
The positive root is: . levels
The greatest depth is: . m.