+0  
 
0
242
3
avatar+97 

The population of the human race in 2000 was 6100 million, with an annual growth rate of 1.4%. The population (in millions) as a function of time (years) is described reasonably well by the equation

P(t) = 6100e0.014t

Determine:

 

  • When the population was/will be 2.38 times that at the census date (in years, relative to the census date, with 4 decimal places)
  • The population at that time (in whole millions, as an integer)
  • The rate of growth of the population at that time (in number of individuals per day, as an integer: 1 year has 365.2422 days)

    Years = years
    Pop = million
    Rate = individuals per day

Oli96  Oct 28, 2014

Best Answer 

 #2
avatar+85644 
+13

I get something a little different from Alan, here

The beginning population number doesn't matter, so the first part is.....

2.38P = Pe.014t    divide by P and  take the ln of both sides

ln(2.38) = lne.014t     and by a log property, we have  (remember, lne = 1)

ln(2.38) =.014t   divide both sides by .014

ln(2.38)/.014 = t = 61.9357 years

 

CPhill  Oct 28, 2014
Sort: 

3+0 Answers

 #1
avatar+26625 
+5

P(t) = 6100*e0.014t

dP(t)/dt = 0.014*6100*e0.014t

t = ln(P/6100)/0.014

 

P = 2.38*6100 

$${\mathtt{t}} = {\frac{{ln}{\left({\frac{{\mathtt{2.38}}{\mathtt{\,\times\,}}{\mathtt{6\,100}}}{{\mathtt{6\,100}}}}\right)}}{{\mathtt{0.014}}}} \Rightarrow {\mathtt{t}} = {\mathtt{61.935\: \!749\: \!120\: \!241\: \!666\: \!2}}$$

t = 61.9357 years

$${\mathtt{dPdt}} = {\frac{{\mathtt{0.014}}{\mathtt{\,\times\,}}{\mathtt{6\,100}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{0.014}}{\mathtt{\,\times\,}}{\mathtt{61.935\: \!7}}\right)}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{6}}}}{{\mathtt{365.242\: \!2}}}} \Rightarrow {\mathtt{dPdt}} = {\mathtt{556\,485.149\: \!380\: \!397\: \!522\: \!958\: \!7}}$$

dP/dt = 556485 individuals per day

 

(Edited to correct the expression for t)

.

Alan  Oct 28, 2014
 #2
avatar+85644 
+13
Best Answer

I get something a little different from Alan, here

The beginning population number doesn't matter, so the first part is.....

2.38P = Pe.014t    divide by P and  take the ln of both sides

ln(2.38) = lne.014t     and by a log property, we have  (remember, lne = 1)

ln(2.38) =.014t   divide both sides by .014

ln(2.38)/.014 = t = 61.9357 years

 

CPhill  Oct 28, 2014
 #3
avatar+26625 
+10

Thanks Chris, I forgot the 0.014 in my original calculation of t.  I've now corrected that.

.

Alan  Oct 28, 2014

16 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details