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 , 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.
B. Merton will have about 6,000 more people than Hapville.
In the year 2030, which is 30 years since 2000, the population of Hapville will be 18,000 + (500*30) = 33,000 people.
For Merton, the population in the year 2030 can be found by plugging in t=30 into the equation y = 12.5(1.08)^t.
So, y = 12.5(1.08)^30 = 12.5(5.632) = 70.4 thousand people, which is 70,400 people.
Therefore, Merton will have 70,400 - 33,000 = 37,400 people more than Hapville in 2030.
37,400 people = 37.4 * 1,000 = 37,400 people.
So, Merton will have about 6,000 more people than Hapville in 2030.