# Thread: Exponential growth and decay question

1. ## Exponential growth and decay question

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).
What will the percentage rate of decline in population be after 10 years?

(k = ln(0.9)/-4

2. ## Re: Exponential growth and decay question

The picture is not there.

Are you given the initial population of the city at $t=0$?

3. ## Re: Exponential growth and decay question

that is the whole first bit of the question, it then asks
a) Show that P(t)=P(t(subscript 0))e^-kt is a solution of the differential equation dP(t)/dt = -KP(t)
and
b) What percentage decline will there be after 10 years, given a 10% decline in 4 years? (answer = 23%)
and then c) as above, no initial value

4. ## Re: Exponential growth and decay question

Assuming you have done a) and b), you would have

$P(t) = P(t_0)e^{t/4\,\log(0.9)}$

Then substitute $t=10$ and you will get the population $P(10)$ after 10 years as a percentage of the original population $P(t_0)$.

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•