Another word problem: when will the population reach 20K?

[Guest]

As I said these are not my forte(?) so any input would be awesome!!

The population of Cedar Rapids is expanding at a rate of P = P(sub 0) e^kt, where P(sub 0) is the current population, k is the expansion rate and t is time (in years). If the populations were 10,000 in 1990 and 12,000 in 2000, when will it reach 20,000?

Thanks!!
Andrea

 

[stapel]

From the phrasing of the exercise, it would appear that 1990 is t = -16 (t = 0 being "current" time, 2006). So plug (t, P) = (-16, 1000) into the equation. Then plug the year-2000 values into the equation.

This gives you two equations in two unknowns, P₀ and k. Solve the system.

Then set P equal to 20,000, and solve for the time t.

Eliz.

 

[Guest]

I totally do not get this one, I understand your explanation of where t is derived but that is where my understanding stops. Am I to be solving multiple equations? I just do not get these.

:?
Andrea

 

[stapel]

Am I to be solving multiple equations?

Yes; two equations in two unknowns. Start off with the plug-n-chug explained earlier. If you get stuck, please reply showing how far you have gotten.

I just do not get these.

We cannot provide classroom instruction within this environment, but we can easily provide links to appropriate lessons. Which topics would you be needing? Exponential functions? Compound growth? Solving systems of equations?

Thank you.

Eliz.