Find the half-life of a radioactive substance that decays by 2% in 6 years

Question

Round to one decimal point

Answer 1

Let's say we start with m units of the substance.

After 6 years, we'll have 0.98m units.

After x years, we'll have (0.98)^x/6m units.

We want to find x so that (0.98)^x/6 = 0.5

Taking logs on both sides,

log (0.98) · x/6 = log (0.5)

Multiply both sides by 6/log (0.98) to get

x = 6 log (0.5)/log (0.98)

= 205.9 years, to one decimal place.