math problem help

Question

The radioactive decay of a substabce is A(t)=600e^-.0013t.

 

A. How many grams of substance was there initially?

 

B. How much is left after 50 years?

 

C. What is the half-life?

 

Answer 1

A.

600 gm

B.

A(50) = 600e^-0.0013(50)

A(50) = 600e^-0.065

A(50) ≈ 600(0.937)

A(50) ≈ 562.24

C.

300 = 600e^-0.0013t

0.5 = e^-0.0013t

ln 0.5 ≈ 0.0013t

1.60 ≈ 0.0013t

1238.0 ≈ t 

Answer 2

A(t) = 600 e^(-0.0013t)

 

A.

 

A(0) = 600 e^(0) = 600 g

 

B.

 

A(50) = 600 e^[-0.0013(50)] = 600 e^(-0.065) = 562.24 g

 

C.

 

0.5 = e^(-0.0013 t_1/2)

 

t_1/2 = ln(0.5) / (-0.0013) years = 533.19 years