1. **State the problem:** We need to check if the population in 2021, calculated by adding the same absolute increase from 2001 to 2011, matches the claim that the population increases by the same percentage from 2011 to 2021. 2. **Calculate the percentage increase from 2001 to 2011:** The population increased from 420000 to 480000. Increase = $480000 - 420000 = 60000$ Percentage increase = $$\frac{60000}{420000} \times 100 = \frac{60000}{420000} \times 100 = 14.29\%$$ 3. **Calculate the expected population in 2021 using the same percentage increase:** Expected increase from 2011 to 2021 = $$480000 \times \frac{14.29}{100} = 480000 \times 0.1429 = 68592$$ Expected population in 2021 = $$480000 + 68592 = 548592$$ 4. **Compare Liam's calculation:** Liam added the same absolute increase (60000) to 480000 and got 540000. 5. **Conclusion:** Liam's method assumes the population increases by the same absolute amount, but the claim is about the same percentage increase. Since $$548592 \neq 540000$$, Liam's population of 540000 does not match the claim. **Final answer:** No, the population of 540000 does not match the claim because the percentage increase method gives 548592.