To find out how the populations of Hapville and Merton compare in 2030, we will calculate the populations of both towns in that year.
For Hapville:
- The population in the year 2000 = 18,000.
- The population increases by 500 people per year.
- From 2000 to 2030 is 30 years.
The population of Hapville in 2030 can be calculated as follows:
\[ \text{Population in 2030} = 18,000 + (500 \times 30) = 18,000 + 15,000 = 33,000 \]
For Merton:
- The population follows the equation \( y = 12,000(1.04)^t \), where \( y \) is in thousands and \( t \) is the number of years since 2000.
- For 2030, \( t = 30 \).
Using the formula:
\[ y = 12,000(1.04)^{30} \]
We need to calculate \( (1.04)^{30} \):
\[ (1.04)^{30} \approx 3.243 \]
Now substitute back into the equation:
\[ y = 12,000 \times 3.243 \approx 38,916 \text{ (in thousands)} = 38,916 \]
Comparing populations:
- Hapville population in 2030: 33,000
- Merton population in 2030: 38,916
Now we find the difference:
\[ 38,916 - 33,000 \approx 5,916 \]
This means Merton will have approximately 5,916 more people than Hapville in 2030.
Thus, the closest answer choice is:
B. Merton will have about 6,000 more people than Hapville.