1. **State the problem:** We have an initial number of users $P_0 = 330$ on a website, growing exponentially at an annual rate of 51%. We want to write a function $P(t)$ representing the number of users after $t$ years. 2. **Formula for exponential growth:** The general formula is $$P(t) = P_0 \times (1 + r)^t$$ where $r$ is the annual growth rate as a decimal. 3. **Calculate the function:** Here, $r = 0.51$, so $$P(t) = 330 \times (1 + 0.51)^t = 330 \times 1.51^t$$ 4. **Find the daily rate of change:** Since $t$ is in years, and there are 365 days in a year, the daily growth factor $a$ satisfies $$1.51 = a^{365}$$ Taking the 365th root, $$a = 1.51^{\frac{1}{365}}$$ 5. **Calculate $a$ rounded to 4 decimal places:** $$a = e^{\frac{\ln(1.51)}{365}} \approx e^{\frac{0.4121}{365}} \approx e^{0.001129} \approx 1.00113$$ 6. **Write the function with daily time $d$ in days:** $$P(d) = 330 \times 1.00113^d$$ 7. **Calculate the daily percentage rate of change:** $$\text{Daily rate} = (a - 1) \times 100 = (1.00113 - 1) \times 100 = 0.113\%$$ Rounded to the nearest hundredth of a percent, this is $0.11\%$ per day. **Final answers:** - Function for users after $t$ years: $$P(t) = 330 \times 1.51^t$$ - Daily growth function: $$P(d) = 330 \times 1.00113^d$$ - Daily percentage rate of change: $0.11\%$ per day.