Please answer both questions.

Question

A radioactive element is such that N grand remain after t hours, where N =12^-0.031t

 

A.) how many grand are inItaly present? 

B.) after how many hours are there 6 grams of the element left. 

Answer 1

Mohammed,

Please, please check over your submitted questions for typographical errors before you send them! If you don't care enough to submit an error-free question, why would someone care enough to help you find an error-free answer? And more importantly for the future, who would want to hire you, if you can't even be bothered to check your own work for errors?

Grand is not the same as grams!

inItaly is not the same as initially!

Now for some hints: A) "initially" means at the start, before any time has passed. So you need t=0 hours; substitute that in your equation and solve it (Google will even do the math for you, if you can write it correctly!).

B) You have an equation in two variables (N and t). Where do you think the value "6" should be substituted? Assuming you've done that correctly, how do you then go about finding the value of t for that equation (hint: you need to do something to bring t out of being in an exponent, and of course if you do that operation to one side of an equation, you have to do it to the other, also -- otherwise, they wouldn't stay equal!). Once you've done that, then you need to get t all alone -- so how do you reverse t getting multiplied by -0.031 ?

Hope this helps you in a number of ways; feel free to provide feedback.

Answer 2

I think you intended to type "Divide both sides by 12 to get...." 

Answer 3

N(t) = 12e^-0.031t

 

Initial amount  = N(0) = 12e⁰ = (12)(1) = 12 grams.

 

When will 6 grams remain?

 

Solve the equation 6 = 12e^-0.031t

 

Divide both sides by 12 to get 0.5 = e^-0.031t

 

Take natural log of both sides:  ln(0.5) = ln(e^-0.031t)

 

Since ln(e^-0.031t) = -0.031t, we have t = ln(0.5)/(-0.031)

 

So, t ≈ 22.4 hours