Question 1053741: The population of Stratford is growing exponentially. In the year 2005, the population was 235,000 people. In the year 2016 the population had grown to 308,340.
a) Find the equation that models the growth of the city
b) Predict the population of the city in the years 2025 and 2000
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! y=ab^x. where x=11 years
235000(1+rate)^11=308340
divide by 235000 to get 1.312, but don't round until end.
(1+r)^11=1.312
take ln of both sides
11 ln (1+r)=ln 1.312
11 ln (1+r)=0.2716
divide by 11 again 0.02469
ln(1+r)=0.02469
now raise to the e power, and 1+r=1.025
r=0.025 or 2.5%, rounding at the end.
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Check
235000*(1.025^11)=308340.36
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2025 will be 20 years
235000*(1.025^20)=385,075, rounding at end
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2000 is 5 years earlier.
235000=(1+0.025)^5*x
235000/(1.025^5)=x
207,706 was the population in 2000.
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