SOLUTION: The population of Dallas County, which follows the exponential growth model, increaed from 491,675 in 2000 to 782,341 in 2010. A- Find the exponential growth rate, k. B- Write

Question 1075515: The population of Dallas County, which follows the exponential growth model, increaed from 491,675 in 2000 to 782,341 in 2010.
A- Find the exponential growth rate, k.
B- Write the exponential growth funtion. Use growth rate found in a.
C- What should the population be in 2016? Use function from b.
D- When should the population be 999,999? use the funtion from b.
E- How long will it take the population to double? Use growth rate found in A.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
A. 782341/491675=1.5911750648294096710225250419484, or a growth rate of 59% over 10 years. So:
(1+k)^10=1.5911750648294096710225250419484
ln (1+k)^10= ln 1.5911750648294096710225250419484
10 ln(1+k)=ln 1.5911750648294096710225250419484
ln(1+k)=ln 1.5911750648294096710225250419484/10=0.04644727777645335179835425806392
e^0.04644727777645335179835425806392=1+k
k=1.0475428488243655419718940009655, or 4.75428488243655419718940009655% growth rate per year.
B. Population year t=491675 x (1.0475)^(t-2000)
C. Population in 2016=491675 x (1.0475)^16=1033100.64 people
D. 999999=491675 x (1.0475)^(t-2000)
2.0338617989525601260995576346164=(1.0475)^(t-2000)
By the previous process we get t=15.298251227477130099351978599649, or the desired population of 999999 somewhere soon after January, 2015.
E.For the initial population to double, we have:
2=1.0475^t
ln 2=ln 1.0475^t
ln 2=t ln 1.0475
t=approximate 15.3 years for the population to double at the current rate. ☺☺☺☺
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