Question

A certain substance decays so that it loses 15% of its material each year.
After 3 years, how much of an initial 40 grams would be left?

Answer 1

Since you need to find this for only 3 years, not 20 or 30, you can just take off 15% three times.

Answer 2

But the next question asks for the equation you used and I'm not sure how to get that.

Answer 3

Ok, we can figure that out.
If you had a problem that was:
"A book costs $40. The store gives 15% discount. What is the price after the discount?"
How would you solve it?

Answer 4

I would just subtract 40(.15) from 40

Answer 5

Good. That is one way of doing it.
Another way of doing it is this:
The full price of the book, $40, is 100% of the price.
Since the discount is 15%, then 100% - 15% = 85%, that means we only need to pay for 85% of the price.
If you calculate 85% of $40, you will get the same result as 40 - 0.15(40)

Answer 6

100% as a decimal is 1.
15% as a decimal is 0.15
100% - 15% = 85%
As a decimal, 1 - 0.15 = 0.85
The discounted price is 40*0.85

Answer 7

After 1 year, the the 40 grams are now 0.85 * 40 grams.
After 2 years, it goes down by another 15%, so 0.15 * 40 grams becomes 0.85 * 0.85 * 40 grams
As you can see, each year that passes, you multiply by another 0.85, to show that 85% of the material is left (which means the same as 15% of the material is lost.)

Answer 8

So it's 24.565 grams?

Answer 9

This suggests a formula:
N = B(1 - r)^t
where N = new amount after t years
B = beginning amount
r is the rate of decay written as a decimal

Answer 10

You are correct.

Answer 11

I'm so stupid I got it right the first time then .-. But when I checked it I got 22, must've checked it wrong lol