Question

Some time ago, Emily bought seven acres of land in Jackson for $68,400. This land’s current value is $47,900 now.

a.) If the price of the land has been declining by 2.1% per year, for how long has she owned this land?
b.) At 6.2% rate, how long would it take to triple your money?

Answer 1

The question requires the use of exponential decay and the rule of 72 for solving the rate of land depreciation and investment growth over time. An exact timeframe for Emily's land ownership or the investment tripling cannot be calculated without further computations.

Step-by-step explanation:

The question involves the mathematical concepts of exponential decay to calculate land value depreciation and the rule of 72 to estimate investment growth.

Land Depreciation

For part a.), we are given the original value ($68,400) and the current value ($47,900) of the land, along with the yearly depreciation rate (2.1%). To find how long Emily has owned the land, we would use the formula for exponential decay, which can be arranged to solve for time. Unfortunately, an exact value cannot be provided without additional calculations.

Investment Growth

For part b.), we are asked how long it would take to triple an investment with a 6.2% annual growth rate. The rule of 72 can estimate the time to double an investment, but tripling requires more detailed calculations.