SOLUTION: in 2000, the population of a city was 74,000 the population has grown to 123,000 by 2010, when the population will reach 178000. Report the number of years after 2000

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Question 1093343: in 2000, the population of a city was 74,000 the population has grown to 123,000 by 2010, when the population will reach 178000.
Report the number of years after 2000

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming a constant, geometric growth rate, the formula for which is P_1=P_0*e^kt, where P_0 is the initial population, P_1 is the resultant population, k is the constant growth rate, and t is time, then:
123000=74000*e^10k
So:
1.6621621=e^10k
ln 1.6621621=ln e^10k=10k ln e=10k
k=1n 1.6621621/10=0.0508119
178000=74000*e^0.0508119t
2.4054054054054054054054054054054=e^0.058119t
ln 2.4054054054054054054054054054054= ln e^0.058119t=0.058119t ln e= 0.058119t
t=ln 2.4054054054054054054054054054054/0.058119
t=17.273867 years after 2000
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