Respuesta :
Answer:
The rate of change in number of subscriber for the six years is 3.62%
Step-by-step 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 × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, P = p × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, 8200 = 10225 × [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Or, [tex]\dfrac{8200}{10225}[/tex] = [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Or, 0.80195 = [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Taking power [tex]\dfrac{1}{6}[/tex] both side
So, [tex](0.80195 )^{\frac{1}{6}}[/tex] = [tex]((1 - \frac{r}{100} )^{6})^{\frac{1}{6}}[/tex]
Or, 0.9638 = 1 - [tex]\dfrac{r}{100}[/tex]
Or, [tex]\dfrac{r}{100}[/tex] = 1 - 0.9638
Or, [tex]\dfrac{r}{100}[/tex] = 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
