An atom of 32.3 nanograms becomes 8% smaller every minute due to extreme radiation. how many nanogtama will it be in half an hour

There will be about 2.64750838 in 30 mins

Hello! So, for this question, we are doing exponential decay. The formula for exponential decay is P (1 - r) ^t, where P is the initial amount, r is the rate, and t is the time, in this case, minutes. 8% is 0.08 in decimal form. The atom becomes 8% smaller every minute, but we still have 92% of it left or 0.92 in decimal form, because 1 - 0.08 is 0.92. As you probably know, half an hour is 30 minutes. We will raise 0.92 to the 30th power, because we are talking about the amount of decay in 30 minutes. 0.92^30 is 0.081966204. This is a long decimal, but do not delete this long decimal from the calculator. Now, we must multiply that by 32.3 to get the amount. When we do that, we get 2.647508376 or 2.6 when rounded to the nearest tenth. There. There will be approx. 2.6 nanograms of an atom after half an hour.