Answer:
a) 0.5198 computers per household
b) 0.01153 computers
Step-by-step explanation:
Given:
number of computers in a home,
q = 0.3458 ln x - 3.045 ; 10,000 ≤ x ≤ 125,000
here x is mean household income
mean income = $30,000
increasing rate,
= $1,000
Now,
a) computers per household are
since,
mean income of $30,000 lies in the range of 10,000 ≤ x ≤ 125,000
thus,
q = 0.3458 ln(30,000) - 3.045
or
q = 0.5198 computers per household
b) Rate of increase in computers i.e ![\frac{dq}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdq%7D%7Bdt%7D)
= ![\frac{d(0.3458 ln x - 3.045)}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%280.3458%20ln%20x%20-%203.045%29%7D%7Bdt%7D)
or
![\frac{dq}{dt}=0.3458\times(\frac{1}{x})\frac{dx}{dt} - 0](https://tex.z-dn.net/?f=%5Cfrac%7Bdq%7D%7Bdt%7D%3D0.3458%5Ctimes%28%5Cfrac%7B1%7D%7Bx%7D%29%5Cfrac%7Bdx%7D%7Bdt%7D%20-%200)
on substituting the values, we get
![\frac{dq}{dt}=0.3458\times(\frac{1}{30,000})\times1,000](https://tex.z-dn.net/?f=%5Cfrac%7Bdq%7D%7Bdt%7D%3D0.3458%5Ctimes%28%5Cfrac%7B1%7D%7B30%2C000%7D%29%5Ctimes1%2C000)
or
= 0.01153 computers