There are 14.30 elements is remaining after 13 minutes, to the nearest 10th of a gram.
Given
An element with a mass of 970 grams decays by 27.7% per minute.
What is the rate of decay?
The rate of decay for radioactive particles is a first-order decay process. This means it follows an exponential decay pattern.
The exponential decay is represented by the following formula;
\(\rm Remaining \ elements = Mass (1- rate)^{Time}\)
Substitute all the values in the formula;
\(\rm Remaining \ elements = Mass (1- rate)^{Time}\\\\\rm Remaining \ elements = 970 (1- \dfrac{27.7}{100})^{13}\\\\Remaining \ elements = 970 (\dfrac{100-27.7}{100})^{13}\\ \\ Remaining \ elements = 970 (\dfrac{72.3}{100})^{13}\\\\ Remaining \ elements = 970 (0.723)^{13}\\ \\ Remaining \ elements = 970 \times 0.0147\\\\Remaining \ elements =14.30\)
Hence, there are 14.30 elements is remaining after 13 minutes, to the nearest 10th of a gram.
To know more about the Rate of decay click the link given below.
https://brainly.com/question/14231923
