HELP...i can't get it! Algebra?

you are in a group of city planners that is trying to determine whether or not to expand an electrical power plant. To aid your decision, you will use the information from the last two census figures for the city, showing a population of 100,525in 1990 and 126,422 in 2000. Knowing that the current electrical plant can produce enough electricity for 175,000 people, use the formula N(t)= Pe^kt to determine during what year the plant will no longer meet the needs of your city.

Ultimately, you want to find out what the value of t is when N(t) = 175,000. But you don't know what P and k are. So use the data they give to set up two equations. To make this easier, let 1990 be t=0. This means 2000 is t=10.

100,525 = Pe^(k*0)
126,422 = Pe^(k*10)

The first one simplifies to 100,525 = P. Use this value in the second equation and solve for k. Then use both P and k in the equation 175,000 = Pe^(kt), and solve for t. Remember that this is the number of years since 1990, so add the t value to 1990.

I already showed you how to do that here

http://answers.yahoo.com/question/index;...

One way to solve this is to find P and k in the formula, then use the formula to find the year given the population. If you let time t be number of years after 1990 this becomes a bit easier:

Use the 1990 data:

100525 = P e^k*0, or 100525 = P *1

so P = 100525

Use the 2000 data:

126422 = 100525 e^10*k, or

e^10*k = 126422/100525 = 1.256

take the natural log of both sides:

10*k = 0.229 so k = 0.0229

so we use these (P=100525 & k=0.0229) in the formula, also using the population of 175000 and solving for t:

175000 = 100525 e^0.0229t
ln (1.74) = 0.0229t
0.554/0.022 = t = 24.2

So the population would be too big for the power plant about 24 years after 1990, or sometime in 2014.