Malthus' principle of population growth can be written as the differential equation?

Question

y'=ky

where y(t) is the population t years after the initial measurement and k is the growth constant. The solution to this differential equation is given by

y(t)=Ae^(kt)

where A is the initial amount. If k = 0.03, determine the annual percent increase in y.

what is the Annual percent increase ?

Answer 1

e^0.03 = 1.030454534, which is a 3.0454534% increase.

Answer 2

This is the 3 percent. With the exponential function, in 33.3 years, the population will increase to "eA". This is a compounded effect, and the formula for compound interest will yield the same result with a 3 percent increase/

Answer 3

Approximately 3%. For small values of k, exp(k) is approximately equal to 1+k. (You can get a slightly better value with a scientific calculator.) So, if the population was 6 billion at this time last year, you would now expect it to be 6.18 billion.

Answer 4

ok, we know that y(t) = Ce^(kt) (bear with me, i use C instead of A)

if k = 0.03, and it is the ANNUAL inscrease, it means that it is to be measured for one year. So, we've got Ce^.03
that gives us 1.03045...C
Therefore, then annual increase is 3.045%.