Ask Question
17 September, 02:04

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?

+3
Answers (2)
  1. 17 September, 03:15
    0
    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
  2. 17 September, 04:26
    0
    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
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “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 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers