Question

An element with mass 430 grams decays by 27.4% per minute. How much of the element is remaining after 19 minutes, to the nearest 10th of a gram?

Answer 1

First, we subtract 27.4 from 100, which gives us 72.6.  After each generation, we will have 72.6% of the last generation.  Now, we do 430 * .726^19.  This equals 1.0 grams.

Answer 2

We have been given an element with mass 430 grams decays by 27.4% per minute. We are asked to find the amount of element remaining after 19 minutes.

We will exponential decay formula to solve our given problem.  

An exponential decay function is in form $y=a\cdot (1-r)^x$, where

y = Final value,

a = Initial value,

r = Growth rate in decimal form,

x = Time.    

$27.4\%=\frac{27.4}{100}=0.274$

We can see that initial value is 430, so our required function would be $y=430\cdot (1-0.274)^x$.

$y=430\cdot (0.726)^x$

To find amount of element after 19 minutes, we will substitute $x=19$ in our function as:

$y=430\cdot (0.726)^{19}$

$y=430\cdot (0.002279270099677)$

$y=0.980086$

Upon rounding to nearest tenth of gram, we will get:

$y\approx 1.0$

Therefore, approximately 1.0 grams of the element will be remaining after 19 minutes.