1. **State the problem:** You are asked to solve the exponential function $f(t) = 480(1.0082)^t$ and choose the correct answer from options A-D. 2. **Formula and explanation:** The function models exponential growth with initial value 480 and growth factor 1.0082 per unit time $t$. 3. **If the question is to find $f(t)$ for a specific $t$, plug in the value of $t$ and calculate. For example, if $t=10$: $$f(10) = 480(1.0082)^{10}$$ 4. **Calculate the power:** $$1.0082^{10} \approx 1.085$$ 5. **Multiply:** $$f(10) = 480 \times 1.085 = 520.8$$ 6. **If the question is to find $t$ for a given $f(t) = y$, use logarithms:** $$y = 480(1.0082)^t$$ Divide both sides by 480: $$\frac{y}{480} = (1.0082)^t$$ 7. **Take logarithm of both sides:** $$\log\left(\frac{y}{480}\right) = \log\left((1.0082)^t\right)$$ 8. **Use log power rule:** $$\log\left(\frac{y}{480}\right) = t \log(1.0082)$$ 9. **Solve for $t$:** $$t = \frac{\log\left(\frac{y}{480}\right)}{\log(1.0082)}$$ 10. **Choose the correct answer A-D based on the calculated value or given options.** **Final answer depends on the specific value or options given.**