1. **State the problem:** We are given the function $f(t) = 480(1.0082)^t$ and asked to solve it. Usually, solving such a function means finding $f(t)$ for a given $t$ or finding $t$ for a given $f(t)$. 2. **Formula and explanation:** This is an exponential growth function where 480 is the initial value and 1.0082 is the growth factor per unit time $t$. 3. **Example: Find $f(t)$ for a specific $t$:** Suppose we want to find $f(10)$. 4. **Calculate:** $$f(10) = 480(1.0082)^{10}$$ 5. **Intermediate step:** Calculate the power first: $$1.0082^{10} \approx 1.085$$ 6. **Multiply:** $$f(10) = 480 \times 1.085 = 520.8$$ 7. **Answer:** For $t=10$, $f(t) \approx 520.8$. If you want to solve for $t$ given $f(t)$, use logarithms: 8. **Solve for $t$ given $f(t) = y$:** $$y = 480(1.0082)^t$$ Divide both sides by 480: $$\frac{y}{480} = (1.0082)^t$$ 9. **Take logarithm:** $$\log\left(\frac{y}{480}\right) = \log\left((1.0082)^t\right)$$ 10. **Use log power rule:** $$\log\left(\frac{y}{480}\right) = t \log(1.0082)$$ 11. **Solve for $t$:** $$t = \frac{\log\left(\frac{y}{480}\right)}{\log(1.0082)}$$ This formula allows you to find $t$ for any given $f(t) = y$. **Summary:** The function models exponential growth with base 1.0082 and initial value 480. You can calculate $f(t)$ for any $t$ or find $t$ for any $f(t)$ using logarithms.