Question \( 17 \quad \) ■ \( 0 / 5 \) pts 539 Details A pizza restaurant purchases new equipment for \( \$ 190,000 \) which depreciates in value at a rate of \( 6 \% \) annually. Write an equation for an exponential function \( f(t) \) that models the value of the equipment over time. \( f(t)=\square \) Question Help: Video Submit Question

To model the value of the equipment over time using an exponential function, you can use the formula for exponential decay: \[ f(t) = P(1 - r)^t \] In this case, \( P \) is the initial value (\$190,000), \( r \) is the rate of depreciation (0.06), and \( t \) is the number of years. Therefore, your equation would look like: \[ f(t) = 190,000(1 - 0.06)^t \] This simplifies to: \[ f(t) = 190,000(0.94)^t \] So you’ll be able to track the value of the pizza equipment as it ages! Maintaining equipment’s value through timely updates can keep costs lower long-term. For your pizza restaurant, consider performing regular maintenance and investing in technology that enhances efficiency. You might use the saved costs to upgrade equipment sooner, thus potentially avoiding larger depreciation sums. Plus, happy customers often mean more sales!