A county has 2,500 high school students. The County built a new high school with a capacity for 3,200 students. If the student population grows at 4% per year, how long until the new school is full? (Round to the nearest tenth.)
2500 * 1.04^n >= 3200
1.04^n >= 1.28
n >= 6.29 years
To find out how long it will take for the new high school to be full, we need to determine the rate at which the student population grows each year and calculate how many years it will take for the population to reach the school's capacity.
Step 1: Calculate the annual increase in the student population.
The student population grows at a rate of 4% per year. So, we need to find 4% of the current student population to determine the number of additional students each year.
4% of 2,500 = (4/100) * 2,500 = 0.04 * 2,500 = 100
Step 2: Calculate the number of years it takes for the school to reach capacity.
Since the annual increase is 100 students, we can calculate the number of years it will take for the population to grow from 2,500 to 3,200 students by dividing the difference in student population by the annual increase.
3,200 - 2,500 = 700
700 / 100 = 7
Therefore, it will take approximately 7 years for the new school to be full.
Note: Keep in mind that this calculation assumes a constant growth rate of 4% each year, and it does not account for any other factors that may affect student population growth, such as migration or changes in birth rates.