An element with a mass of 100 grams decays by 20.5% per minute. To the nearest minute, how long will it be until there are 10 grams of the element remaining?

About 10 minutes.

Step-by-step explanation:

Let's make an equation to model this situation. This is called exponential decay, so we'll need to use an exponent soon. We're starting with 100 grams:

100

It decays (this means subtraction) by 20.5% per minute. With m = minute:

100 (1 -.205) ^m

And we want to end up with 10 grams remaining:

100 (1 -.205) ^m = 10

Let's solve for m now!

100 (1 -.205) ^m = 10

(1 -.205) ^m = 10/100

.795^m =.1

log. 795 (.1) = m

m = 10.037 = about 10 minutes

Every minute, the mass is reduced by 20.5%, making it 79.5% of the new mass. We can use this to set up an equation where x = minutes.

100 * (0.795) ^x = 10

Solve for x.

Divide by 100 on both sides

0.795^x = 1/10

log (0.795^x) = log (1/10)

x * log (0.795) = log (1/10)

x = log (1/10) / log (0.795)

x ≈ 10

10 minutes