Population Word Problem

[darshanpatel]

1. The problem statement, all variables and given/known data

Let b(t) be the number of births in the United States at the end of year t, and let d(t) represent the number of deaths in the United States at the end of year t. If p(t) is the population of the United States at the beginning of year t, write a function c(t) that represents the percent change in the population of the United States at the end of year t.

2. Relevant equations

none

3. The attempt at a solution

There was no other work I could come up with besides going straight to the answer:

Answer: c(t)= (b(t)-d(t))/p(t)

Please show all work... Thanks!

[Simon Bridge]

Isn't c supposed to be a percentage. Anyway:

The idea of doing a derivation in steps is just to explain your reasoning - show the examiner why you have to be correct.
What you do is break your thoughts down into baby-steps, like you have to explain it to someone smart but ignorant.

initial population = p
final population = p+b-d
change in population = (p+b-d)-p = (b-d)
percentage change = c = 100(b-d)/p

see how if you just go right to the end it kinda looks like you plucked the relation out of thin air, but if you spell it out like this, the reader has more confidence that you know what you are doing?

[darshanpatel]

wait so the answer would be c(t)=(100(b(t)-d(t))/p(t) ? I am turning this into the teacher and he knows for problem like these, there isn't much you can show, So I am good there.

[Simon Bridge]

I have been known to make mistakes include deliberate inconsistencies to make sure a student is alert, so you need to reason it out. The only difference between mine and yours is that factor of 100 - if you know where it comes from, you are sweet.

[darshanpatel]

yeah, the 100 is for getting the percentage, is that right?