1. The problem is to understand and analyze the function $f(t) = 480(1.0082)^t$. 2. This is an exponential function of the form $f(t) = a \cdot b^t$, where $a = 480$ is the initial value and $b = 1.0082$ is the base of the exponential. 3. Since $b > 1$, the function represents exponential growth. 4. The graph of this function will be increasing and curved upwards, starting at $f(0) = 480$ because any number to the zero power is 1. 5. To find specific values, substitute $t$ with the desired input and calculate $f(t)$. 6. For example, at $t=0$, $f(0) = 480 \times 1.0082^0 = 480 \times 1 = 480$. 7. At $t=10$, $f(10) = 480 \times 1.0082^{10}$. Calculate the power first: $1.0082^{10} \approx 1.085$, so $f(10) \approx 480 \times 1.085 = 520.8$. 8. The function has no intercepts with the $t$-axis because it never reaches zero or negative values. 9. The function has no extrema (maximum or minimum points) because it is strictly increasing. 10. The shape of the graph is an increasing exponential curve starting at 480 when $t=0$ and growing slowly as $t$ increases.