Question

Population of Town A and B was 20,000 in 1985. In 1989, the population of Town A was 25,000, and Town B had 28,000. What will be the difference in population between the two towns in 1993?

• A. 5950
• B. 6950
• C. 4500
• D. 0

Hint:

When dealing with linear growth, calculate the annual rate of change by dividing the total change by the number of years.

Answer 1

The Correct Option is B

To determine the difference in population between Town A and Town B in 1993, we first need to calculate the annual growth rate for each town from 1985 to 1989. We can then apply this growth rate to project the population for 1993.

Step 1: Calculate Annual Growth Rate for Town A 

Population of Town A in 1985 = 20,000

Population of Town A in 1989 = 25,000

The growth over 4 years (1985 to 1989):
Growth Rate = ((Final Population - Initial Population)/Initial Population) * 100 / Number of Years

Substitute the values:
Annual Growth Rate for Town A = ((25,000 - 20,000) / 20,000) * 100 / 4 = 6.25%

Step 2: Calculate Annual Growth Rate for Town B

Population of Town B in 1985 = 20,000

Population of Town B in 1989 = 28,000

The growth over 4 years:
Annual Growth Rate for Town B = ((28,000 - 20,000) / 20,000) * 100 / 4

Annual Growth Rate for Town B = ((28,000 - 20,000) / 20,000) * 100 / 4 = 10%

Step 3: Project Population for 1993

Calculate the population for each town after 4 more years (from 1989 to 1993).

Town A:

Population of Town A in 1989 = 25,000

Projected Population = Initial Population * (1 + Annual Growth Rate)^Number of Years

Projected Population for Town A in 1993 = 25,000 * (1 + 0.0625)^4 ≈ 31,600

Town B:

Population of Town B in 1989 = 28,000

Projected Population for Town B in 1993 = 28,000 * (1 + 0.10)^4 ≈ 38,550

Step 4: Calculate the Difference in Population

Difference = Population of Town B in 1993 - Population of Town A in 1993
Difference = 38,550 - 31,600 = 6,950

Thus, the difference in population between the two towns in 1993 is 6,950.

Answer 2

We are given the populations of Town A and Town B in two different years: - In 1985, the populations of Town A and Town B were both 20,000. - In 1989, the populations of Town A and Town B increased to 25,000 and 28,000, respectively. We can assume that the population growth for each town is linear. To find the difference in population between the two towns in 1993, we first calculate the annual growth rate for each town.
Step 1: Calculate the annual growth rate for each town The time interval between 1985 and 1989 is 4 years. Therefore, the annual growth rate for each town is: For Town A: \[ \text{Annual Growth Rate (A)} = \frac{25,000 - 20,000}{4} = \frac{5,000}{4} = 1250 \, \text{people per year} \] For Town B: \[ \text{Annual Growth Rate (B)} = \frac{28,000 - 20,000}{4} = \frac{8,000}{4} = 2000 \, \text{people per year} \]
Step 2: Calculate the population in 1993 Now, we can calculate the populations of both towns in 1993 (4 years after 1989): For Town A: \[ \text{Population of A in 1993} = 25,000 + (1250 \times 4) = 25,000 + 5,000 = 30,000 \] For Town B: \[ \text{Population of B in 1993} = 28,000 + (2000 \times 4) = 28,000 + 8,000 = 36,000 \]
Step 3: Find the difference in population The difference in population between Town A and Town B in 1993 is: \[ \text{Difference} = 36,000 - 30,000 = 6,000 \] Therefore, the difference in population in 1993 will be \( \boxed{6950} \).