1. **State the problem:** We start with 972 infected people, and the virus spreads at a rate of 15% per day. We want to find how many people will be infected after 13 days. 2. **Formula used:** The number of infected people after $t$ days with a daily growth rate $r$ is given by the exponential growth formula: $$ P(t) = P_0 (1 + r)^t $$ where $P_0$ is the initial number of infected people, $r$ is the growth rate as a decimal, and $t$ is the number of days. 3. **Identify values:** - $P_0 = 972$ - $r = 0.15$ - $t = 13$ 4. **Calculate:** $$ P(13) = 972 (1 + 0.15)^{13} = 972 (1.15)^{13} $$ 5. **Intermediate step:** Calculate $(1.15)^{13}$: $$ (1.15)^{13} \approx 6.137 $$ 6. **Multiply:** $$ P(13) = 972 \times 6.137 = 5961.564 $$ 7. **Round to nearest whole number:** $$ \boxed{5962} $$ **Final answer:** After 13 days, approximately 5962 people will have caught the virus.