Question

help me with this problem appliying logarithms applications solving this: the population of a city is growing at a rate proportional to its population. the population 20 years ago was 100 000 and today is it 150 000. find the population 20 years from now.

Answer 1

dp/dt= k p

Answer 2

whats dp/dt=kp

Answer 3

lol, forget it

Just remember this
\[P=P_0 e^{rt}\]

Answer 4

225,000

Answer 5

yes that it i tryed to do it usind this formula but got a decimal number

Answer 6

i like your reply imran.. "lol forget it" lolz :D

Answer 7

imranmeah you didnt explain it at all

Answer 8

so do you get 225 000

Answer 9

15=10 e^20r
find r

r= 3/ 2e^20

Answer 10

r=0.0202733

Ignore last result

100 000 e^(40(0.0202733))=225000...

Answer 11

following the formula I got 1.5=e^20r am I on the right step

Answer 12

can i show you an easier way?

Answer 13

yes but using logs application

Answer 14

we already know how much the population grew by in 20 years

it increased from 100,000 to 150,000

now to work out the percentage it increased by in 20 years

you divide the total number of population now by what it was 20 years ago
so you do this

150,000 / 100,000 = 1.5

1.5 * 100 = 150% it grew by in 20 years

150% / 20 = 7.5% every year (this is irrelevant to this question but just showing how to get percentage for each year if you wanted to know)

now we need to find out how much the population will be after another 20 years

so the population now is 150,000

150,000 * 1.5 = 225,000 we dont need to change the percentage as it is trying to work out for the same amount of time

dont forget to click good answer and this is how i worked it out

Answer 15

hi I need touse the formula imranmeah wrote above I got different result

Answer 16

can you t fo

Answer 17

use the formula