Hello, girlpower1991!

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.

Theseconddifferences are constant.

. . Hence, the function is of theseconddegree . . . a quadratic.

The general quadratic function is: .

Plug in the first three values of the sequence:

. .

Hence: .

We have: .

Quadratic Formula: .

The positive root is: . levels

The greatest depth is: . m.