A population grows exponentially according to the formula A(t)=7,000^0.04t where t is measured in years.

Question

Find the time in years that it takes the population to triple. First give the exactanswer in years and then give the answer to the nearest hundredth of a year.

Answer 1

there may be mistake in the problem. It might really be A(t)=7000e^.04t where 7,000 is the initial population.

then it triples when 21000= 7000e^.04t where 4% is the annual growth rate

3 = e^.04t take natural logs of both sides

ln3 = .04t

t = ln3/.04 =exact number of years = about 27.47 years to triple the population

simple 4% growth would mean in 25 years it doubles. In 50 years it triples, but this is compound growth rate which is like compound interest in shortening the double and triple times

If you really meant

A=7000^.04t

then

3=7000^.04t

then you'd have to take logs of both sides to the base 7000

log7000(3) = .04t

then convert with a change of base

ln3/ln7000 =.04t

t = ln3/ln7000/0.04 = about 3.10 years which makes the city look worse than breeding rabbits

so odds are you really meant A(t) = 7000e^.04t