A county planner is looking at trends in population growth for two towns, Hapville and Merton.
The population of Hapville in the year 2000 was 18,000. Since then, the population has increased at a steady rate of 500 people per year.
The population of Merton is increasing according to the equation y=12,000(1.04)^t , where y = the population in thousands and t = the number of years since the year 2000.
If these trends continue, how will the populations of the two towns compare in 2030?
A.
Hapville will have about 6,000 more people than Merton.
B.
Merton will have about 6,000 more people than Hapville.
C.
Hapville will have about 21,000 more people than Merton.
D.
Merton will have about 21,000 more people than Hapville.
To find the population of Hapville in 2030, we need to add 30 years (since 2000) of growth at 500 people per year to the initial population of 18,000:
Population of Hapville in 2030 = 18,000 + (30 * 500) = 18,000 + 15,000 = 33,000
Now, we need to find the population of Merton in 2030 using the given equation:
Population of Merton in 2030: y = 12,000(1.04)^30 ≈ 12,000 * 2.208 = 26,496
Comparing the populations of Hapville and Merton in 2030, we see that Hapville will have about 6,504 more people than Merton.
Therefore, the correct answer is B. Merton will have about 6,000 more people than Hapville.