Question

An element with mass 490 grams decays by 28.6% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?

Answer 1

Answer:

M1 = M0 * (1 - .286) = .714 M0

M2 = .714 M1 = .714^2 M0

Mn = .714 ^n M0

M16 = .714^16 M0 = .00456 M0 = .00456 * 490 = 2.24 gm

Answer 2

Hence 2.2344 g of the element is remaining after 16 minutes.

Step-by-step explanation:

Given:

An element is having mass of 490 grams decays by 28.6% per minute.

Therefore after each minute, the amount remaining is,

⇒ (100 - 28.6)%

= 71.4%

= $\frac{71.4}{100}$

= 0.714 times as much as was present at the start of the minute.  If t is the number of minutes elapsed from when you had 490 g, then

Hence, the element is remaining after 16 minutes to the nearest 10th of a gram is,

$m(t) = 490 (0.714)^t,$

with t in minutes and m(t) in g

$m(16) = 490 (0.714)^{16} g$

$m(16) = 490 \times 0.00456 g$

m(16) = 2.2344 g

Hence 2.2344 g of the element is remaining after 16 minutes.