Exponential Growth and Decay (1 Viewer)

[oly1991]

The population of a city is P(t) at any one time. The rate of decline in population is proportional to the population P(t), that is, dP(t)/dt=-kP(t).
(a) Show that P(t)=P(t0)e^-kt is a solution to the differential equation dP(t)/dt=-kP(t).
(b) What percentage decline in population will there be after 10 years, given a 10% decline in 4 years?
(c) What will the percentage rate of decline in population be after 10 years?
(d) When will the population fall by 20%?

I did (a) with ease but im having trouble with the others....

 

[oly1991]

anyone?

 

[EvoRevolution]

did u copy the question down correctly
it looks like there is somethin missing

 

[oly1991]

did u copy the question down correctly
it looks like there is somethin missing

yep it's the exact question

 

[oly1991]

This question might help....

A population in a certain city is growing at a rate proportional to the population itself. After 3 years the population increases by 20%. How long will it take for the population to double?

 

[oly1991]

bump

 

[Drongoski]

I'll give it a go:

Edit

Wonder if soln correct; it was done about 5.15 pm yesterday and when I tried to post it I couldn't. Was the BOS site down ??

 

[oly1991]

thank you

 

[Drongoski]

thank you

But what are correct answers ?

 

[oly1991]

But what are correct answers ?

you were right....

i should probably read the question more carefully next time lol

 

[Drongoski]

But note I've solved without the usual approach of finding the value of 'k' first, as is usual in maths books (I think). Instead I worked out the value of e^-k

 

[oly1991]

yeh i saw that...took me a while to figure out what you did.

I tried doing it again by doing it the way i'd been doing it (finding k first) and it went good so i might answer the next question i do your way.

 

[Drongoski]

yeh i saw that...took me a while to figure out what you did.

I tried doing it again by doing it the way i'd been doing it (finding k first) and it went good so i might answer the next question i do your way.

I've been thinking about this type of questions for some time; it occured to me that it made no sense to find 'k' at all but seems the 'normal and safer' way to do so.

 

[oly1991]

I've been thinking about this type of questions for some time; it occured to me that it made no sense to find 'k' at all but seems the 'normal and safer' way to do so.

yeh but you need 'k' to find the rate of decline.