1. **State the problem:** The population growth of mosquitos follows the uninhabited growth model, which is exponential growth without limits. We are given the initial population $P_0 = 1500$ and the population after 24 hours $P(24) = 2500$. We want to find the population after 3 days (72 hours). 2. **Write the growth equation:** The uninhabited growth equation is $$P(t) = P_0 e^{kt}$$ where $k$ is the growth rate and $t$ is time in hours. 3. **Find the growth rate $k$:** Use the known values at $t=24$: $$2500 = 1500 e^{24k}$$ Divide both sides by 1500: $$\frac{2500}{1500} = e^{24k}$$ Simplify the fraction: $$\frac{5}{3} = e^{24k}$$ Take the natural logarithm of both sides: $$\ln\left(\frac{5}{3}\right) = 24k$$ Solve for $k$: $$k = \frac{\ln\left(\frac{5}{3}\right)}{24}$$ 4. **Calculate the population after 72 hours:** Substitute $t=72$ into the growth equation: $$P(72) = 1500 e^{k \times 72} = 1500 e^{72 \times \frac{\ln\left(\frac{5}{3}\right)}{24}} = 1500 e^{3 \ln\left(\frac{5}{3}\right)}$$ Use the property $e^{a \ln b} = b^a$: $$P(72) = 1500 \left(\frac{5}{3}\right)^3 = 1500 \times \frac{125}{27} = \frac{1500 \times 125}{27}$$ Calculate the value: $$P(72) = \frac{187500}{27} \approx 6944.44$$ 5. **Final answer:** The population after 3 days is approximately 6944 mosquitos. The closest choice is **a. 6 944**.