3. You buy a new boat for 36,000 Each year the value of the boat depreciates at a rate of 14% per year. How much will the boat be worth in 7 years? Eqn __ Ans: __

To find the value of the boat after 7 years, we use the formula for exponential depreciation:<br /><br />\[ V = P \times (1 - r)^t \]<br /><br />where:<br />- \( V \) is the future value of the boat,<br />- \( P \) is the initial purchase price of the boat (\$36,000),<br />- \( r \) is the annual depreciation rate (14% or 0.14),<br />- \( t \) is the number of years (7).<br /><br />Plugging in the values:<br /><br />\[ V = 36000 \times (1 - 0.14)^7 \]<br /><br />\[ V = 36000 \times (0.86)^7 \]<br /><br />Now calculate:<br /><br />\[ V = 36000 \times 0.377149515 \approx 13577.38 \]<br /><br />So, the boat will be worth approximately \$13,577.38 in 7 years.