A substance of 50 grams decreases its weight by 1/5 of its weight every minute. How heavy will it be after 4 minutes?

Answer 1

There are a couple ways to calculate this. You could do it step by step, subtracting 1/5 of the total mass each time, but the easier way to do it can be done in one step.

Subtracting 1/5 of something means leaving behind 4/5 of it. 4/5 of something is the same as 80%, or 0.8 times that amount. So, each step of subtracting 1/5 is really just multiplying by 0.8. So 4 minutes, or four repetitions of subtracting 1/5, looks like this:

50 * 0.8 * 0.8 * 0.8 *0.8

Or:

50 * (0.8)^4

This value can easily be calculated as 20.48. So after four minutes, the substance will weigh 20.48 grams.

Answer 2

If you decrease something by 1/5, you are left with 4/5 of the previous amount, right?

50(4/5) = 200/5 = 40 grams left after 1 minute

40(4/5) = 160/5 = 32 grams after 2 minutes

50(4/5)⁴ = 50(256/625) = 12,800/625 ≈ 20 grams