Question: Susan monitors the number of strep infections reported in a certain neighborhood in a given week. The recent numbers are shown in this table: Week Number of People 0 20 1 26 2 34 3 44 According to her reports, the reported infections are growing at a rate of 30%. If the number of infections continues to grow exponentially, what will the number of infections be in week 10?

1. **State the problem:** We want to find the number of infections in week 10, given that infections grow exponentially at a rate of 30% per week. 2. **Formula for exponential growth:** The number of infections at week $t$ is given by $$N(t) = N_0 \times (1 + r)^t$$ where: - $N_0$ is the initial number of infections, - $r$ is the growth rate (as a decimal), - $t$ is the number of weeks. 3. **Identify known values:** From the table, at week 0, $N_0 = 20$ infections. The growth rate is $r = 0.30$ (30%). 4. **Calculate the number of infections at week 10:** $$N(10) = 20 \times (1 + 0.30)^{10} = 20 \times 1.30^{10}$$ 5. **Calculate $1.30^{10}$:** Using a calculator, $1.30^{10} \approx 13.786$. 6. **Multiply to find $N(10)$:** $$N(10) = 20 \times 13.786 = 275.72$$ 7. **Interpretation:** Since the number of infections must be a whole number, we round to the nearest whole number: **Final answer:** $$\boxed{276}$$ infections are expected in week 10 if the exponential growth continues.