A rare baseball card was purchased for \( \$ 280,000 \) and has been increasing in value at a rate of \( 6 \% \) per year. Write an equation for an exponential function \( f(t) \) that models the value of the rare baseball card after \( t \) years. \( f(t)= \)

To model the value of the baseball card over time, the equation for an exponential function can be formed using the initial value and the growth rate. Since the card was purchased for \( \$ 280,000 \) and is increasing at a rate of \( 6\% \) per year, you can express the function as: \( f(t) = 280,000 \cdot (1 + 0.06)^t \) or simplified to: \( f(t) = 280,000 \cdot (1.06)^t \) This equation shows how the value of the card will grow exponentially over the years as time \( t \) progresses. To visualize it further, after just a few years, that baseball card could potentially soar to stratospheric values; after 10 years, for instance, the card's value could exceed \( \$ 500,000 \)! It’s like watching your investment grow before your very eyes, just like a vine climbing higher as the seasons change!