Question

The population of Ketcham High School has been decreasing by 5% per year. If its population is currently 2600 students, which of the following is closest to its population two years from now?

(1) 2,340
(2) 2,470
(3) 2,347
(4) 2,590

Answer 1

To estimate Ketcham High School's population in two years with a yearly decrease of 5%, we successively calculate 5% of the population each year and subtract it from the current population. After two years, the closest estimate is 2,347 students.

Step-by-step explanation:

The question involves calculating the estimated population of Ketcham High School two years from now, given a yearly decrease of 5%. To solve this, we apply the concept of a percent decrease to the current population of 2,600 students.

For the first year, we find 5% of 2,600:

1. 5% of 2,600 = 0.05 × 2,600 = 130
2. Subtract this decrease from the original population to get the population after one year: 2,600 - 130 = 2,470
3. For the second year, again find 5% of the new population: 5% of 2,470 = 0.05 × 2,470 = 123.5, which we can approximate to 124 for simplicity.
4. Subtract this decrease from the population after the first year: 2,470 - 124 = 2,346.

Thus, the closest answer to the population two years from now is 2,347 students, which corresponds to option (3).