The Thumber of people with the flu during an epidemic is a function, \( f \), of the number of days, \( d \), since the epidemic began. The equation \( f(d)=50 \cdot\left(\frac{3}{2}\right)^{d} \) defines \( f \). a. How many people had the flu at the beginning of the epidemic? Select Choice \( \checkmark \) b. How quickly is the flu spreading? Each day, the number of infected people grows by a factor of Select Choice \( \vee \). c. What does \( f(1) \) mean in this situation? This represents the number of people with the flu 1 day Select Choice \( \checkmark \) the epidemic began.

Let's address each part of the problem step by step. --- ### **a. How many people had the flu at the beginning of the epidemic?** To find the number of people who had the flu at the **beginning** of the epidemic, we evaluate the function \( f(d) \) at \( d = 0 \) days. \[ f(0) = 50 \cdot \left(\frac{3}{2}\right)^{0} = 50 \cdot 1 = 50 \] **Answer:** **50 people** had the flu at the beginning of the epidemic. --- ### **b. How quickly is the flu spreading?** The function \( f(d) = 50 \cdot \left(\frac{3}{2}\right)^{d} \) indicates exponential growth. The base of the exponential term, \( \frac{3}{2} \), represents the **daily growth factor**. \[ \text{Daily Growth Factor} = \frac{3}{2} = 1.5 \] **Answer:** Each day, the number of infected people grows by a factor of **\( \frac{3}{2} \)** (or **1.5 times**). --- ### **c. What does \( f(1) \) mean in this situation?** Evaluating \( f(1) \) gives the number of people infected **1 day** after the epidemic began. \[ f(1) = 50 \cdot \left(\frac{3}{2}\right)^{1} = 50 \cdot \frac{3}{2} = 75 \] **Interpretation:** \( f(1) \) represents the number of people with the flu **1 day after** the epidemic began. --- **Summary of Answers:** - **a.** 50 people - **b.** Each day, the number grows by a factor of \( \frac{3}{2} \) - **c.** The number of people with the flu 1 day after the epidemic began