halflife

[thegoatherder13]

half life of palladium-100 is 4 days. the initial mass is 1 gram.. how do i go about finding the mass after t number of days?

 

[soroban]

Hello, Goatherder!

Half-life of palladium-100 is 4 days. The initial mass is 1 gram.
How do i go about finding the mass after t number of days?

It depends on what course you are in.

If you are in Differential Equatons, you are expected to derive the formula.

If you are in an earlier course, you should have been <u>given</u> a formula.


Given: .inltial mass A_o and half-life h, then: k = (ln 2)/h

. . the amount remaining (A) after time t is given by: .A .= .A_oe^-kt


Your problem has: .A_o = 1, .h = 4, .k = (ln 2)/4 ≈ 0.173

. . . Therefore: .A .= .e^-0.173t

 

[thegoatherder13]

im in calc 1.. but not given a formula

 

[stapel]

Then think back to algebra, where you first encountered exponential growth and decay.

You know the equation is "A = Pe^rt". You know you first have to find the decay constant "k". So plug in the half-life info and solve for k.

Then re-write the equation, using the given value for P and your derived value for k. This is your function.

Eliz.

. . . . .Exponential Word Problems

 

[thegoatherder13]

i dont get where u r coming from..

 

[thegoatherder13]

for my equation i got 1/2^t/4 ??

 

[stapel]

I'm sorry, but I don't understand your post. Your fraction appears to have three parts to it, but a fraction should have only a numerator and a denominator. Also, an "equation" has an "equals" in it.

To see "where I was coming from", you might want to review your notes and/or text from algebra, re-read the section in your calculus book, and/or follow the link (provided earlier) showing worked examples of this type.

Eliz.