Question

If the mass of a sample of radioactive material is given by m=800*2^(-0.04t)... grams, time in years
a) What is the initial mass?
b) After how long time is the mass 50g

Answer 1

a: Initial mass should be 800 grams.

Answer 2

Yes, I realise this. More interested in b), thanks (:

Answer 3

a) 800 b) 100 years

Answer 4

Solution?

Answer 5

solution is to solve
\[800\times2^{-0.04t}=50\] for \(t\)

Answer 6

step 1) is to divide both sides by 800 and get
\[2^{-0.04t}=\frac{1}{16}\]

Answer 7

step 2) is to recognize that \(\frac{1}{16}\) is an integer power of 2, namely -4 because
\(2^{-4}=\frac{1}{16}\) and final step is to set
\[-0.04t=-4\] and solve for \(t\)