Problem Solving

hi guys

please could you explain me this issue?

The population of a certain town increases by 50% every 50 years
If the population in 1950 was 810, in what year was the population 160?

thks

I think there should be a better method than this one do this question but anyways:
population in 1950 = 810

we need to find the year of population 160

Lets say the year was 19xx and population = 160
population increases by 1/2 of the previous population every year so
in 19xx+1, population was = 160+160/2 = 240
in 19xx+2, population was = 240+240/2 = 360
in 19xx+3, population was = 360+360/2 = 540
in 19xx+4, population was = 540+540/2 = 810
so 19xx+4 = 1950
19XX = 1946

Let me know if this makes sense

the kaplan s explanation wasnt good at all below

" population in 1950 was 150% so 3/2 ??of the 1900 POPULATION

this means the 1900 population was 2/3? of 1950 population
similary the 1850 population was 2/3 of 1900 population, and so on.
"

why 2/3??

francoisph wrote:the kaplan s explanation wasnt good at all below

" population in 1950 was 150% so 3/2 ??of the 1900 POPULATION

this means the 1900 population was 2/3? of 1950 population
similary the 1850 population was 2/3 of 1900 population, and so on.
"

why 2/3??

Think of 2/3 this way.

Pretend we start with 10
Now let's increase that number by 50%
The new number would be 15 right.

Now, let's pretend we need to return back to 10.
If we times 15 by 2/3 we get 10

To reverse a 50% increase we have to decrease the new number by 33%, because the new number is larger.

Does that make sense?

yeah it makes senses now !

thks

indiantiger wrote:I think there should be a better method than this one do this question but anyways:
population in 1950 = 810

we need to find the year of population 160

Lets say the year was 19xx and population = 160
population increases by 1/2 of the previous population every year so
in 19xx+1, population was = 160+160/2 = 240
in 19xx+2, population was = 240+240/2 = 360
in 19xx+3, population was = 360+360/2 = 540
in 19xx+4, population was = 540+540/2 = 810
so 19xx+4 = 1950
19XX = 1946

Let me know if this makes sense

Oh just now read the post above. The population increase by 50% every 50 years. So it decreases by 33% going backwards

1950 - 810
1900 - 540
1850 - 360
1800 - 240
1750 - 160

So 1750 should be the answer

exponential growth formula:

x(t)=ab^(t/T)

a=x(time 0)
b=factor of increase
t=time to x(t)
T=time for x to increase by factor of b

810=160*(1.5)^(t/50)
t=200 yrs

@ jeffedwards,

Thanks for the correction, it has been a long day

indiantiger wrote:@ jeffedwards,

Thanks for the correction, it has been a long day

you were mostly all on...i do that all the time