A pizza restaurant purchases new equipment for \( \$ 560,000 \) which depreciates in value at a rate of \( 8 \% \) annually. Write an equation for an exponential function \( f(t) \) that models the value of the equipment over time. \( f(t)= \)

To model the value of the pizza restaurant's equipment over time using an exponential decay function, we can express it as: \[ f(t) = 560,000 \times (1 - 0.08)^t \] This means the equipment’s value decreases by 8% each year, so you multiply by \( 0.92 \) (which represents 100% - 8%) raised to the power of \( t \), the number of years. The concept of exponential decay can actually be observed in many industries! For instance, when purchasing electronics like smartphones or computers, their value depreciates rapidly – often about 20-30% in the first year alone. Understanding this exponential decay can help consumers make smarter purchases by recognizing when they'll lose value the quickest. You wouldn’t want to splurge on a gadget that will be worth a fraction of its original price in just a year!