decay - check exponential model is correct

Question

half life of m-50 is 8 hrs, and you have 50 grams.  "A" is number of hrs after recording and f(A) is the amt left. describe this with an exponential model.  

 

I have:  50 * 1/2 ^a/8 is this right?

 

 

use a radical notation to show what is the rate of decay of this element every hour ?

 

I have:  the eight root of 25 is 1.495 ;I dont think this is right?

Answer 1

f(A) = 50*(1/2)^(A/8) is correct

 

To find the decay rate per hour you need to find the ratio of f(A+1) to f(A) 

 

f(A+1) = 50*(1/2)^((A+1)/8)

           = 50*(1/2)^(A/8 + 1/8)

           = 50*(1/2)^(A/8) * (1/2)^(1/8)  

           = f(A) * (1/2)^(1/8)  

 

So F(A+1) / f(A) = (1/2)^(1/8) which is the eighth root of (1/2) ~ 0.917

Answer 2

f(A) = 50(0.5)^A/8

Rate of decay per hour is (0.5)^1/8 , or ⁸√0.5.