Differential equations

Hi, i need help wth this question. TIA x

Presuming youre starting at a? So when it says rate of increase (change) what terms might be involved?

k & x

Assuming x is the population, how do you express the rate of change/increase? How do you represent the 0.5% of x? No idea what k is.

0.5x? Or 0.5kx?

0.5x is a half of x and still no idea what k is. Theres also no differential term or an equation.

Do you have an example in your textbook (like radioactive decay or ...) which describes a simple differential equation?
https://math24.net/radioactive-decay.html
This obviously decreases, but it has some similarities with what you want.

wait so what is the answer? Kx/2?

Dy/dx = 0.5x

Its not right, but it is a differential equation at least. What do y and x represent and 0.5x is still not 0.5%. Why not try and try and describe what youre thinking?

I'm thinking that k = 0.005 coz it's says that it increases by 0.5%
x = population size
And y = population of country

0.005 as a multiplier is right. Whether you call it k is a red herring, but if x is the population size, then 0.005x is 0.5% of the peopulation.
However, look back to the radioactive decay example and think about the variables in the derivative on the left hand side of the equation and how they relate to the right. It should be similar for your case.

I don't really understand that example. So the answer for a is dy/dx = 0.005x, correct?

No - where is time in your equation?

Time?

Rate of increase ....

Ohh so should it be dy/dt = 0.005t

Not quite.. Youve written the right hand side as 0.5% of time, rather than the population. Again, look at the radioactive decay example, or your textbook.

I'm just going round in circles omds. So dy/dx = 0.005xt ?