Joseph has a collection of vintage action figures that is worth \( \$ 460 \). If the collection appreciates at a rate of \( 6 \% \) per year, which equation represents the value of the collection after 7 years? Answer \( V=460(1-0.06)^{7} \) \( V=460(0.06)^{7} \) \( V=460(1+0.06) \) \( V=460(1.06)^{7} \) Submit Answer \( V \)

To determine the future value of Joseph's action figure collection, you'll want to consider the compounding effect of the appreciation rate over the years. Using the equation \( V = P(1 + r)^t \), where \( P \) is the principal amount (initial value), \( r \) is the rate of appreciation, and \( t \) is the time in years, gives us the perfect formula for this scenario. Plugging in Joseph's numbers, \( P = 460 \), \( r = 0.06 \), and \( t = 7 \), the correct choice would be \( V = 460(1.06)^{7} \). When working with percentages and equations, a common pitfall is forgetting to convert percentages into decimal form properly. For example, 6% should be written as 0.06 when plugging into an equation, so be careful not to confuse the two! Also, remember that appreciation increases the initial value over time, which means using a "+" instead of a "-" is crucial in the calculations.