# population growth question using a symetric difference quotient

• July 28th 2010, 09:05 AM
bemidjibasser
population growth question using a symetric difference quotient
If the symetric difference quotient is given as: (P'(t)= P(t+10)-P(t-10)/20)
Given the info below, how would I compute this equation? I am a little lost and getting a bit frustrated... I am not sure what to use for (P'(t)... Any help would be greatly appreciated...

Date population at t time in years after 1790
1790 3.9 t=0
1800 5.3 t=10
1810 7.2 t=20
1820 9.6 t=30
1830 12.9 t=40
• July 29th 2010, 03:55 AM
CaptainBlack
Quote:

Originally Posted by bemidjibasser
If the symetric difference quotient is given as: (P'(t)= P(t+10)-P(t-10)/20)
Given the info below, how would I compute this equation? I am a little lost and getting a bit frustrated... I am not sure what to use for (P'(t)... Any help would be greatly appreciated...

Code:

```Date        population at t      time in years after 1790        1790            3.9                      t=0 1800            5.3                      t=10 1810            7.2                      t=20 1820            9.6                      t=30 1830            12.9                      t=40```

$P'(10)=\dfrac{P(20)-P(0)}{20}=\dfrac{7.2-3.9}{20}$

$P'(20)=\dfrac{P(30)-P(10)}{20}=\dfrac{9.6-5.3}{20}$

etc

CB
• July 29th 2010, 06:31 AM
bemidjibasser
Thanks CB! Much appreciated!