chiuda said:
It is an equation to do with population growth it asks approximately when (t- time in years) will population(p) be 175 000
I honestly can't figure it out this is far as i get
p(t)=6t^4-5t^3+200t+12000
175000=6t^4-5t^3+200t+12000
0=6t^4-5t^3+200t-163000I honestly don't know what to do i am lost, I'm sure its not that complicated but i just would love some help.
Thanks in advance!:)
The question asks you for an approximate value, so a good way to go would be to plot p(t) and pick out where it equals 175,000. The exact solution to this problem is horrible: here is what Maple 14 gets for the smallest positive root of p(t) = 175000:
root =
5/24-1/24*((25*(414180+4380*5388398241^(1/2))^(1/3)-40*(414180+4380*5388398241^(1/2))^(2/3)
+18772800)/(414180+4380*5388398241^(1/2))^(1/3))^(1/2)
+ 1/24*10^(1/2)*((5*(414180+4380*5388398241^(1/2))^(1/3)*((25*(414180+4380*5388398241^(1/2))^(1/3)
-40*(414180+4380*5388398241^(1/2))^(2/3)+18772800)/(414180+4380*5388398241^(1/2))^(1/3))^(1/2)
+4*((25*(414180+4380*5388398241^(1/2))^(1/3)
-40*(414180+4380*5388398241^(1/2))^(2/3)+18772800)/(414180+4380*5388398241^(1/2))^(1/3))^(1/2)*(414180+4380*5388398241^(1/2))^(2/3)
-1877280*((25*(414180+4380*5388398241^(1/2))^(1/3)-40*(414180+4380*5388398241^(1/2))^(2/3)
+18772800)/(414180+4380*5388398241^(1/2))^(1/3))^(1/2)
+11495*(414180+4380*5388398241^(1/2))^(1/3))/(414180+4380*5388398241^(1/2))^(1/3)/((25*(414180+4380*5388398241^(1/2))^(1/3)
-40*(414180+4380*5388398241^(1/2))^(2/3)+18772800)/(414180+4380*5388398241^(1/2))^(1/3))^(1/2))^(1/2)
It is an irrational number. The other real root is a negative irrational, and there are also two complex conjugate irrational roots.
Nowadays we don't need to worry much about problems like this one because of ready availability of powerful computer methods. For example, if you have EXCEL you can get a numerical solution easily using the Solver tool. Many hand-held calculators would be able to do this problem with no difficulty. If all those tools are unavailable to you, you can still submit the problem to Wolfram Alpha, which costs you nothing if you already are paying for internet access.
RGV