A population was decreasing at a rate of 6% per month. What is the annual decay rate? Enter your answer, rounded to the nearest tenth of a percent, in the box

Hello there! So, we will be doing this through exponential decay. The formula for exponential decay is I (1 - r) ^t, where r = rate per month, t = amount of times decayed, and I = initial amount. 6% is 0.06 in decimal form. 1 - 0.06 is 0.94. The population decreases 6% per month and 94% of the previous population remains each month. Annual is over a year and there are 12 months in 1 year. It will decay 12 times in one year, so we will raise 0.94 to the 12th power. Solve this on your calculator. 0.94^12 is 0.475920315. It's a long decimal, but don't delete it yet. To turn it into percent form, multiply by 100 to get 47.59203 and other numbers behind it or 47.6 when rounded to the nearest tenth. There. The annual rate of decay is about 47.6%.

Note: To explain the formula better, when it comes to exponential decay, you subtract the percent in decimal form from 1, raise to the t power, depending on how many times it decays over a period of time, and then if you have a population, then you multiplying by that decimal, but DO NOT delete the long decimal from the calculator. You could make a mistake if you do.