Answer:
13.5 years
Step-by-step explanation:
We are given the expression:
W(x)= 20 x (0.95)^x
Where W(x) = 20grams/2
= 10 grams
Hence:
10 = 20 x (0.95)^x
Divide both sides by 20
10/20 = 20 x (0.95)^x/20
0.5 = (0.95)^x
Take the log of both sides
log 0.5 = log (0.95)^x
log 0.5 = x log (0.95)
Divide both sides by log 0.95
x = log 0.5 / log 0.95
x = 13.513407334 years
Approximately to 1 decimal place =✓13.5 years
Therefore, it will take 13.5 years for the radioactive substance to be half of its original weight.
