An element with the mass of 650 grams decay by 22.6% per minute. to the nearest minute, how long will it be until there are 40 grams of the element remaining

11 minutes.

Step-by-step explanation:

Let x be the number of minutes.

We have been given that an element with the mass of 650 grams decay by 22.6% per minute.

As mass of the element is decaying 22.6% per minute, so this situation can be modeled by exponential function.

Since an exponential function is in form: , where,

a = Initial value,

b = For decay b is in form (1-r), where r is decay rate in decimal form.

Let us convert our given decay rate in decimal form.

Upon substituting our given values in exponential decay function we will get,

Therefore, the function represents the remaining mass of element (y) after x minutes.

To find the number of minutes it will take until there are 40 grams of the element remaining we will substitute y=40 in our function.

Let us divide both sides of our equation by 650.

Let us take natural log of both sides of our equation.

Using logarithm property we will get,

Therefore, it will take 11 minutes to until there are 40 grams of the element remaining.