If we let C(t)=C0e.029t and T(t)=T0e.0518t be the growth models for the two populations then they will be equal at t=t* so C(t*)=T(t*) so C0e.029t*=T0e.0518t* so we now want to solve this equation for t*.
I got (.0518-.029)t*=Ln(C0/T0) so t*=Ln(1.48)/(.0228)=17.2 years. This assumes that the growth rate difference remain constant in time.
Regards
Jim
Peter H.
Hi,
I think the answer is fundamentally correct, but I believe there is one issue -- the student's question is confusing regarding the "growth rate" values. It seems you have interpreted the values of 5.18% and 2.9% to be YEARLY values. That is, 5.18% per year (TX) and 2.9% per year (CA). However, checking population statistics -- for example, TX at
https://www.tsl.texas.gov/ref/abouttx/census.html
I compute that the TX growth rate is reasonably steady at 1.6 to 1.8% per year over the past 6 years or so. Thus, the stated "5.18%" is not a yearly value, it is a total over the 3-year period of 2010 to 2013. I believe the same is true for the CA value; 2.9% is a 3-year total.
Regards, Pete
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07/23/14
Jim S.
tutor
Hi Pete,
Many of the questions posted here are ambiguous to say the least especially with units of measure. You went the extra mile and cleared up the confusion. So the answer is actually 3*17.2 or 51.6 yrs.
Thanks
Jim
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07/23/14
Peter H.
Thanks for the update Jim. Best wishes, Pete
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07/23/14
Cocojas S.
Pete, you are correct in assuming that the growth rate is for the entire 3 year period, as I started my question with "From 2010 to 2013" and I never mention "yearly."
This makes sense and I appreciate the feedback!. Thanks for your answer.
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07/24/14
Peter H.
07/23/14