In 1626,Peter Minuit of the Dutch West India Company purchased Manhattan Island from Native Americans for $24. Assuming an exponential rate of inflation of 6% per year,how much will Manhattan be worth in 2010?

To calculate the worth of Manhattan in 2010, we need to use the formula for calculating compound interest.

The formula for calculating compound interest is:

Final Amount = Principal Amount × (1 + Interest Rate)^Number of Years

Given that the initial purchase price of Manhattan Island was $24 and the inflation rate is 6% per year, we can plug these values into the formula.

Interest Rate = 6% = 0.06
Number of Years = 2010 - 1626 = 384

Final Amount = $24 × (1 + 0.06)^384

To simplify this calculation, we can use a calculator or spreadsheet software to raise (1 + 0.06) to the power of 384.

Using such a tool, we find that (1 + 0.06)^384 ≈ 4,248.78.

Plugging in this value, the equation becomes:

Final Amount = $24 × 4,248.78

Calculating this multiplication, we find that the worth of Manhattan Island in 2010, based on an assumed exponential rate of inflation of 6% per year, would be approximately $101,955.12.