Chapter 9.9, Problem 25PPS

a.

To determine

To find a function to represent number of subscribers to the sports blog after t years.

Answer to Problem 25PPS

  $f(t)=385{\left(1+\frac{93.5}{100}\right)}^t$

Explanation of Solution

Given information:

Sport blog has 395 subscribers

Rate of increase subscribers in sport blog 30 per month

Formula used:

people after t years

  $=P{\left(1+\frac{r}{100}\right)}^t$

P is initial people

r rate of increase of people

t is time in years

Calculation:

Initial people $=385$

Rate of increase of people per month $=30$

In one year 360 subsciber increase

Then total subscribers after one year $=385+360$

on solving,

  $=745$

Rate for one month

  $r=\frac{30\times 100}{385\times 1}$

on solving,

  $r=7.79$

Rate for one year

  $r=7.79\times 12=93.5\%$

Using formula function of sport blog after t years

  $f(t)=385{\left(1+\frac{93.5}{100}\right)}^t$

b.

To determine

To find a function to represent number of subscribers to the photography blog after t years.

Answer to Problem 25PPS

  $g(t)=590{\left(1+\frac{15}{100}\right)}^t$

Explanation of Solution

Given information:

  $f(t)=385{\left(1+\frac{93.5}{100}\right)}^t$

  $g(t)=590{\left(1+\frac{15}{100}\right)}^t$

Rate of increase subscribers in sport blog 15% per year

Formula used:

people after t years

  $=P{\left(1+\frac{r}{100}\right)}^t$

P is initial people

r rate of increase of people

t is time in years

Calculation:

Initial people $=590$

Rate of increase of people per year $=15\%$

Using formula function of photography subscribers

  $g(t)=590{\left(1+\frac{15}{100}\right)}^t$

c.

To determine

To find $(f+g)(x)=f(t)+g(t)$ .

Answer to Problem 25PPS

  $(f+g)(t)=385{\left(1+\frac{93.5}{100}\right)}^t+590{\left(1+\frac{15}{100}\right)}^t$

Explanation of Solution

Given information:

function of sports subscribers

  $f(t)=385{\left(1+\frac{93.5}{100}\right)}^t$

function of photography subscribers

  $g(t)=590{\left(1+\frac{15}{100}\right)}^t$

Calculation:

function of sports subscribers

  $f(t)=385{\left(1+\frac{93.5}{100}\right)}^t$

function of photography subscribers

  $g(t)=590{\left(1+\frac{15}{100}\right)}^t$

  $(f+g)(x)=f(t)+g(t)$

Substituting value of function of photography subscribers and function of sports subscribers

  $(f+g)(t)=385{\left(1+\frac{93.5}{100}\right)}^t+590{\left(1+\frac{15}{100}\right)}^t$

It represent total subscribers after t years

d.

To determine

To find the value of $(f+g)(6)$ .

Answer to Problem 25PPS

  $(f+g)(6)=2174$

Explanation of Solution

Given information:

Find the value of $(f+g)(6)$

  $(f+g)(t)=385{\left(1+\frac{93.5}{100}\right)}^t+590{\left(1+\frac{15}{100}\right)}^t$

Calculation:

  $(f+g)(6)=385{\left(1+\frac{93.5}{100}\right)}^6+590{\left(1+\frac{15}{100}\right)}^6$

On solving,

  $(f+g)(6)=385{\left(1.935\right)}^6+590{\left(1.15\right)}^6$

On solving,

  $(f+g)(6)=2174$