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

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.

Answer 2

What remains of the element after 19 minutes is 1 gram.

What does decay mean?

Decay means when the volume of a mass declines with time. If a mass decays by 10% in a hour, after an hour, the mass would be 90% of the initial volume.

What is the volume of the element after 19 minutes?

The formula for calculating future value:

FV = P (1 - r)^n

• FV = Future value
• P = present mass
• R = rate of decay
• N = number of minutes

430(0.726)^19 = 0.98 grams = 1 gram.

To learn more about decay, please check: https://brainly.com/question/18760477