To calculate how much of the element remains after 16 minutes, we can use the formula for exponential decay:
A(t) = A0 * e^(rt)
Where:
A(t) = amount of substance remaining after time t
A0 = initial amount of substance
r = decay rate
t = time in minutes
e = Euler's number, approximately 2.71828
Given:
A0 = 780 grams
r = 16.3% or 0.163 (as a decimal)
t = 16 minutes
Plugging in the values, we get:
A(16) = 780 * e^(-0.163*16)
A(16) = 780 * e^(-2.608)
Using a calculator, we find that e^(-2.608) ≈ 0.0744
Therefore, A(16) ≈ 780 * 0.0744 ≈ 58.032 grams
Therefore, approximately 58.0 grams of the element is remaining after 16 minutes.
An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?
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1 answer