1. **State the problem:** We are given the number of cases on 1 August as 2284 and on 31 August as 45464. We need to find the daily rate of increase $r$ (expressed as a decimal) assuming exponential growth over 30 days. 2. **Formula used:** The general formula for exponential growth is: $$ N = N_0 (1 + r)^t $$ where: - $N$ is the final number of cases, - $N_0$ is the initial number of cases, - $r$ is the daily rate of increase, - $t$ is the number of days. 3. **Apply the formula:** Given: $$ N_0 = 2284, \quad N = 45464, \quad t = 30 $$ Substitute into the formula: $$ 45464 = 2284 (1 + r)^{30} $$ 4. **Solve for $r$:** Divide both sides by 2284: $$ \frac{45464}{2284} = (1 + r)^{30} $$ Calculate the left side: $$ 19.9 \approx (1 + r)^{30} $$ Take the 30th root of both sides: $$ 1 + r = 19.9^{\frac{1}{30}} $$ Calculate: $$ 1 + r \approx e^{\frac{\ln(19.9)}{30}} $$ $$ \ln(19.9) \approx 2.99 $$ $$ 1 + r \approx e^{\frac{2.99}{30}} = e^{0.0997} \approx 1.1048 $$ Therefore: $$ r = 1.1048 - 1 = 0.1048 $$ 5. **Interpretation:** The daily rate of increase from 1 August to 31 August is approximately 10.48%. 6. **Compare with previous rate:** Previously, the daily increase was 15%. Now it is about 10.48%, which is lower. 7. **Conclusion:** The preventative measures have had a positive effect as the daily infection rate decreased from 15% to approximately 10.48%. This shows the spread of the virus slowed down. **Final answer:** The estimated daily rate of increase from 1 August to 31 August is approximately 10.48%. The preventative measures have positively reduced the infection rate.