Exponential growth and decay question (1 Viewer)

[jadg]

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

 

[fan96]

The picture is not there.

Are you given the initial population of the city at ?

 

[jadg]

Sorry it wont upload
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

 

[fan96]

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



Then substitute and you will get the population after 10 years as a percentage of the original population .