Question

Hey guys! Does any one know how to solve the second part? Thanks.

The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 10% in 10 years. What will be the population in 50 years? (Round your answer to the nearest person.)

How fast is the population growing at
t = 50?

Answer 1

Let the population at time t be denoted by P(t). The rate of population growth is then P'(t), or dP/dt. Since the population growth rate is proportional to the present population, you get the differential equation
\[\frac{dP}{dt}=kP,\]
where k is the constant of proportionality. Do you know how to find the general solution P?

Answer 2

Wait, are you asking about the second question, "How fast is the population growing at t = 50?" Or do you need help with the rest too?

Answer 3

aliter u can use

500(1+.01)^50 =822 appx