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

Using the exponential function, the time take to have 10 grams of the element left is 10 minutes.

Using the expression function :

Plugging the values into the function :

Divide both sides by 100

Take the log of both sides

t = (-1 ÷ −0.099632)

t = 10.036

t = 10.0 minutes

Therefore, the time taken in other to have 10 grams left is 10 minutes.

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Step-by-step explanation:

Step 1   Given   0 times 2 = 0

Step 2 (-4+4)2=0

Step 3 Use The Distributive property

Step 5  Subtract 8 from both sides

Step 6      -4 times 2 = -8