Question

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 1

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

Answer 2

The element takes 19.78 minutes to reach 200 grams, if an element with a mass of 840 grams decays by 7% per minute.

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,

`F = P(1-r)^(t)`..........................(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,

`200 = 840 (1-0.07)^(t)`

`(200)/(840) = (1-0.07)^(t)`

`0.238095= (0.93)^(t)`

Take log on both sides,

㏒ 0.238095 = (t) ㏒ 0.93

-0.6232493 = (t) (-0.03151705)

`t = ( -0.6232493 )/( -0.03151705 )`

= 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.