Question

A scientist found that the height of a mountain increased by approximately 5 x 10⁻⁴ meters each month. If this rate of change continues, by how many meters will the height of the mountain increase in 1 year?

A) 6 x 10⁻³
B) 6 x 10⁻⁴
C) 6 x 10⁻⁵
D) 12 x 10⁻⁴
E) 17 x 10⁻⁴

Answer 1

The height of the mountain will increase by 6 x 10⁻⁳ meters in one year, by multiplying the monthly increase (5 x 10⁻⁴ meters) by the number of months in a year (12). Therefore, the correct option is B.

Step-by-step explanation:

To find the increase in the height of the mountain over one year, we need to multiply the monthly increase by the number of months in a year.

The rate of height increase per month is 5 x 10⁻⁴ meters. There are 12 months in a year, so the total height increase is:

1. Multiply the rate of increase (5 x 10⁻⁴ meters) by the number of months in a year (12).
2. Calculate the product: 5 x 10⁻⁴ meters/month x 12 months = 60 x 10⁻⁴ meters.
3. Simplify the expression: 60 x 10⁻⁴ = 6 x 10⁻⁳ meters.

Therefore, the height of the mountain will increase by 6 x 10⁻⁳ meters in one year.