Respuesta :
The element takes 19.78 minutes to reach 200 grams, if an element with a mass of 840 grams decays by 7% per minute.
Step-by-step explanation:
The given is,
Mass of an element.
Decays by 7% per minute.
Step: 1
Formula to calculate the mass of element with an decay rate after some time period,
[tex]F = P(1-r)^{t}[/tex]..........................(1)
Where, F - Mass of element after t period
P - Mass of element at initial
r - Rate of decay of element
t - Time in minutes
Step: 2
From the give values,
F = 200 grams
P = 840 grams
r = 7 % per minute
Equation (1) become,
[tex]200 = 840 (1-0.07)^{t}[/tex]
[tex]\frac{200}{840} = (1-0.07)^{t}[/tex]
[tex]0.238095= (0.93)^{t}[/tex]
Take log on both sides,
㏒ 0.238095 = (t) ㏒ 0.93
-0.6232493 = (t) (-0.03151705)
[tex]t = \frac{ -0.6232493 }{ -0.03151705 }[/tex]
= 19.77498
t ≅ 19.78 minutes
Result:
The element takes 19.78 minutes to reach 200 grams, if an element with a mass of 840 grams decays by 7% per minute.
An element with a mass of 840 grams decays by 7% per minute. To the nearest minute, how long will it be until there are 200 grams of the element remaining?
Answer: 20
