Question

1. The population,P, in thousands, of a country is P=10^8(1.5)^t/20 where t is measured in years. How long will it take for the population to increase 125 percent?(Hint: If the population increases by 100 percent, it doubles.)

2. How long would it take for a P10,000 investment to double if it earns 12% annual interest compounded annually?

3.
2.25 = 1(10^8) 1.5^(t/20)
since the time would be same for a small country or a large country to increase by 124%, we can ignore the 10^8
take log of both sides
log 2.25 = l log 1.5^(t/20
log 2.25 = (t/20) log 1.5
log2.25/log 1.5 = t/20
t = 20(log2.25)/log 1.5 = 40 years

2 = 1.12^t
easier than the first one, try it

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