The most recent census for a city indicated that there were 867,771 residents. The population of the city is expected to increase at an annual rate of 3.2 percent each year for the next 8 years. What will the population be at that time?Single choice
A
1,189,055
B
1,136,773
C
1,116,459
D
1,152,186
E
1,160,473

Question

The most recent census for a city indicated that there were 867,771 residents. The population of the city is expected to increase at an annual rate of 3.2 percent each year for the next 8 years. What will the population be at that time?Single choice

A

1,189,055

B

1,136,773

C

1,116,459

D

1,152,186

E

1,160,473

BlackTom AI · Accepted Answer

Question restatement: A city has 867,771 residents now, with an annual growth rate of 3.2% for 8 years. What is the population after 8 years?

Approach: Use compound growth. Future population = current population × (1 + growth rate)^(number of years) = 867,771 × (1.032)^8. The exact multiplier (1.032)^8 is approximately 1.286, so the result is roughly 867,771 × 1.286 ≈ 1,115,000 to 1,117,000.

Option-by-option analysis:
- Option A: 1,189,055
  This is significantly higher than the approximated result. If you test by division, 1,189,055 ÷ 867,771 ≈ 1.37, which would imply an average annual growth rate well above 3.2% over 8 years, so this overstated figure is unlikely.
- Option B: 1,136,773
  Closer than A but still notably above the rough estimate. If we check the multiplier, 1,136,773 ÷ 867,771 ≈ 1.309, which corresponds to a higher effective growth rate over 8 years than 3.2%. This suggests the number is too large.
- Option C: 1,116,459
  This aligns with the rough calculation: 867,771 × about 1.286 ≈ 1,115,000–1,117,000. The ratio 1,116,459 ÷ 867,771 ≈ 1.288, which corresponds to a plausible 8-year growth at ~3.2% annually. This is consistent with the expected compound growth.
- Option D: 1,152,186
  Dividing by the starting population gives ≈ 1.328, implying a higher eight-year growth factor than 1.286, thus the implied annual rate would be higher than 3.2% on average. This is unlikely given the stated rate.
- Option E: 1,160,473
  This also implies a growth factor around 1.336, again suggesting a higher average annual rate than 3.2%, making it inconsistent with the given growth rate.

Overall reasoning: The correct computation uses the 8-year compound growth factor (1.032)^8, which yields a multiplier near 1.286. Among the options, the one that matches that expected scale most closely is 1,116,459, while the others are noticeably higher and would require a higher growth rate than 3.2% per year or a miscalculation. The reasoning above shows why the smaller discrepancies in the other numbers are not consistent with the given rate and time horizon.

The most recent census for a city indicated that there were 867,771 residents. The population of the city is expected to increase at an annual rate of 3.2 percent each year for the next 8 years. What will the population be at that time?Single choice

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