Question

a daily newspaper has 10225 subscribers when it began publication. six years old later it has 8200 subscribers what is the average yearly rate of change in the number of subscribers for the six year period

Answer 1

The rate of change in number of subscriber for the six years is 3.62%

Explanation:

Given as :

The initial subscriber of newspaper = p = 10225

The subscriber of newspaper after 6 years of publish = P = 8200

The time period = t = 6 years

Let The average yearly rate of change = r%

Now, According to question

The subscriber of newspaper after n years = initial subscriber ×
`(1-(\textrm rate)/(100))^(\textrm time)`

Or, P = p ×
`(1-(\textrm r)/(100))^(\textrm t)`

Or, 8200 = 10225 ×
`(1-(\textrm r)/(100))^(\textrm 6)`

Or,
`(8200)/(10225)` =
`(1-(\textrm r)/(100))^(\textrm 6)`

Or, 0.80195 =
`(1-(\textrm r)/(100))^(\textrm 6)`

Taking power
`(1)/(6)` both side

So,
`(0.80195 )^{(1)/(6)}` =
`((1 - (r)/(100) )^(6))^{(1)/(6)}`

Or, 0.9638 = 1 -
`(r)/(100)`

Or,
`(r)/(100)` = 1 - 0.9638

Or,
`(r)/(100)` = 0.0362

Or, r = 0.0362 × 100

i.e r = 3.62

So, The rate of change in subscriber = 3.62%

Hence, The rate of change in number of subscriber for the six years is 3.62% . Answer