Question

using loarithms solve:the population of a city is growing at a rate proportional to its population. the population 20 years ago was 100 000 and today it is 150 000. find the population 20 years from now

Answer 1

are you supposed to use
\[P(t)=100,000 e^{rt}\] or an different way?

Answer 2

we can solve this without logarithms if you like

Answer 3

I need to apply logs

Answer 4

20 years in the future i assume

Answer 5

\[\frac{dP}{dt}=P\]
\[\frac{dP}{P}=\ dt\]
\[ln|{P}|=t\]
maybe

Answer 6

just as an exercise in futility ....

ln|P| = t+c

ln|100 000| = -20 + C

C = ln(100 000)+20

ln|P| = 20 + 20 + ln(100 000)

Answer 7

close, but no bananas

Answer 8

we can use
\[\frac{150,000}{100,000}=1.5\] to get a simple answer of
\[P(t)=100,000(1.5)^{\frac{t}{20}}\] where t is years after 20 years ago

Answer 9

actually we dont even need that. we know it increases by 50% every 20 years, so increase 150,000 by 50% to get the answer in one step

Answer 10

the "use logarithms" thing threw me off

Answer 11

me too, i got no idea how to do it with logs

Answer 12

might as well be proximate power and sufficient grace to me lol ... thnx Pascal

Answer 13

i think maybe you are supposed to model this as
\[G(t)=P_0e^{rt}\] and you would find r using logs, but it is silly to do such an easy problem in so many steps

Answer 14

should i use this formula?