Question at position 1 The population of a city is given by P=1000000(1.02)tP = 1000000 (1.02)^t where t is the number of years after 1987. The population in 1989 was:1,004,000.1,002,000.1,040,000.1,040,400.1,020,000.单项选择题
A
1,004,000.
B
1,002,000.
C
1,040,000.
D
1,040,400.
E
1,020,000.

Question

Question at position 1 The population of a city is given by P=1000000(1.02)tP = 1000000 (1.02)^t where t is the number of years after 1987. The population in 1989 was:1,004,000.1,002,000.1,040,000.1,040,400.1,020,000.单项选择题

A

1,004,000.

B

1,002,000.

C

1,040,000.

D

1,040,400.

E

1,020,000.

BlackTom AI · Accepted Answer

We start by identifying the given population model and the time reference.
- The population model is P = 1,000,000 × (1.02)^t, where t is the number of years after 1987.
- To find the population in 1989, we determine t: 1989 − 1987 = 2 years, so t = 2.

Now evaluate P for each option step by step.
Option 1: 1,004,000. This would correspond to multiplying 1,000,000 by 1.004. Since (1.02)^t grows by 2% each year, after 2 years the factor should be (1.02)^2 = 1.0404, which is larger than 1.004. Therefore, 1,004,000 is too small.

Option 2: 1,002,000. This uses a factor of 1.002, which is not consistent with a 2% annual growth over two years. It underestimates the accumulation by a noticeable amount, so this is incorrect.

Option 3: 1,040,000. This corresponds to a factor of 1.04, which is close to (1.02)^2 but not exact. The exact calculation gives 1.0404, so 1,040,000 is slightly lower than the precise value and thus not correct.

Option 4: 1,040,400. This equals 1,000,000 × 1.0404, which matches the exact computation of (1.02)^2 = 1.0404. This aligns with the model given and t = 2 years after 1987.

Option 5: 1,020,000. This would reflect a simple 2% increase once, not compounded over two years. Since the model uses compounding, this linear increase is not appropriate for t = 2 and thus is incorrect.

Putting it together, the options differ by how they model two years of 2% growth and by exact vs approximate factors. The correct factor for two years of 2% growth is (1.02)^2 = 1.0404, which yields 1,040,400 when multiplied by 1,000,000.

Question at position 1 The population of a city is given by P=1000000(1.02)tP = 1000000 (1.02)^t where t is the number of years after 1987. The population in 1989 was:1,004,000.1,002,000.1,040,000.1,040,400.1,020,000.单项选择题

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