The population would grow according to a geometric series. The exact numbers would depend on the rate of growth (some percent per year, or common ratio).

The resources would grow according to an arithmetic series - linear growth. Again, the exact numbers would depend on the rate of growth (some number per year, or common difference).

The formulas are fairly straight forward. But without knowing the rates of growth, this is an impossible question. Did your text or teacher give you any rates you can use for these?

For the geometric (population) series, the term (n=1 fpr 1800, n=101 for the year 1900, and n=201 for the year 2000) is . This can be found with the following formula: where is the first term (1 in this case) and n is the number of the term you want to find. In 1900, for example, the population is: or just . If the population is growing at a rate of 2% per year, for example, then r=1.02. If the population is growing at a rate of 5% per year, then r=1.05. If the population is doubling each year (growing at a rate of 100% per year), then r=2.

For the arithmatic (resource) series, the term (n=1 for 1800, n=101 for the year 1900, and n=201 for the year 2000) is . This can be found with the following formula: where is the first term (1 in this case) and n is the number of the term you want to find. In 1900, for example, the population that could be fed is is: or just . If the amount of resources is increasing by 4 per year, then d=4. If the amount of resources is increasing by 6 per year, then d=6. And so on.