Menu Close

Suppose-the-population-models-of-London-and-Hongkong-in-tens-of-thousands-are-p-t-20t-t-1-and-q-t-240t-t-8-respectively-for-t-years-after-2015-Determine-the-time-period-in-years-when-th

Tinku Tara 0 Comments
Pin




Question Number 77033 by necxxx last updated on 02/Jan/20
Suppose the population models of London and Hongkong in tens of thousands are p(t)=((20t)/(t+1)) and q(t)=((240t)/(t+8)) respectively for t years after 2015, Determine the time period in years when the population of London exceeds that of HongKong.
$${Suppose}\:{the}\:{population}\:{models}\:{of}\:{London} \\ $$$${and}\:{Hongkong}\:{in}\:{tens}\:{of}\:{thousands}\:{are} \\ $$$${p}\left({t}\right)=\frac{\mathrm{20}{t}}{{t}+\mathrm{1}}\:{and}\:{q}\left({t}\right)=\frac{\mathrm{240}{t}}{{t}+\mathrm{8}}\:{respectively}\:{for} \\ $$$${t}\:{years}\:{after}\:\mathrm{2015},\:{Determine}\:{the}\:{time}\:{period} \\ $$$${in}\:{years}\:{when}\:{the}\:{population}\:{of}\:{London} \\ $$$${exceeds}\:{that}\:{of}\:{HongKong}. \\ $$
Commented by MJS last updated on 02/Jan/20
for 2015 (t=0) both are zero?! the limits for x→∞ are p(∞)=20, q(∞)=240 p(t)=q(t) ⇒ t=0∨t=−(4/(11))
$$\mathrm{for}\:\mathrm{2015}\:\left({t}=\mathrm{0}\right)\:\mathrm{both}\:\mathrm{are}\:\mathrm{zero}?! \\ $$$$\mathrm{the}\:\mathrm{limits}\:\mathrm{for}\:{x}\rightarrow\infty\:\mathrm{are}\:{p}\left(\infty\right)=\mathrm{20},\:{q}\left(\infty\right)=\mathrm{240} \\ $$$${p}\left({t}\right)={q}\left({t}\right)\:\Rightarrow\:{t}=\mathrm{0}\vee{t}=−\frac{\mathrm{4}}{\mathrm{11}} \\ $$

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *