Question

thirty percent of a radioactive substance decays in four years. assuming the decay is exponential, find the half life of the substance.
the beginning of 1975 the population of a country was 40 million and growing at a rate of 3% per year. Assume that the growth is exponential. Estimate the population of the country at the beginning of the year 2010

Answer 1

the decay function after t years is

0.3^(t/4)
You want the half-life, or
0.5^(t/k)

0.5^(t/k) = 0.3^(t/4)
t/k log 0.5 = t/4 log 0.3
k = 4log.5/log.3 = 2.3

so, you have (1/2)^(t/2.3)
and thus the half-life is 2.3 years

for the other, the population is

40*1.03^t