College word problem (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 100,25 in 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.

Um... did you mean 100,250 instead of 100,25? If so...

First solve 100,250e^k(10) = 126422

10k = ln(126422/100,250)
k = ln(126422/100,250) / 10

now solve 100,250e^kt = 175,000
e^[ln(126422/100,250) / 10]t = 175,000/100,250
[ln(126422/100,250) / 10]t = ln(175,000/100,250)
t = ln(175,000/100,250) / [ln(126422/100,250) / 10]

Add t to 1990 to find the year where the plant no longer meets the needs.

>>a population of 100,25 in 1990

Missing a digit there?

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