Question

A quantity with an initial value of 3600 decays continuously at a rate of 80% per year.

What is the value of the quantity after 0.2 decades, to the nearest hundredth?

Answer 1

Answer: 726.83

Explanation:

Answer 2

Explanation:

The decay rate of 80% per year means that after each year, the value of the quantity decreases by 80/100 * 3600 = 2880.

To find the value of the quantity after 0.2 decades, we need to multiply the number of years by 10, since a decade is equal to 10 years. In this case, 0.2 decades is equal to 0.2 * 10 = 2 years.

The value of the quantity after 2 years can be found using the formula:

3600 * (1 - 0.8)^2

Plugging in the values, we get:

3600 * (1 - 0.8)^2 = 3600 * (0.2)^2 = 3600 * 0.04 = 144

So, the value of the quantity after 0.2 decades, to the nearest hundredth, is 144.