Chapter 3.4, Problem 61PPS

a.

To determine

To find: Equation that represents the given situation.

Answer to Problem 61PPS

  $A=4200t+3305$ .

Explanation of Solution

Given information:

Number of apps sold in the first week of availability = 3305

On average number of apps sold per hour = 25

From given information

On average number of apps sold per hour = 25

1 day has 24 hours

Therefore

Number of apps sold per day = $24\times 25=600$

We know

1 week has 7 days

Therefore

Number of apps sold per week $=600\times 7=4200$

1 week $\to 4200$ apps

Multiplying with $t$ on both sides

We get

  $\begin{array}{l}\Rightarrow 1\times t\to 4200\times t\\ \Rightarrow t\to 4200t\end{array}$

Therefore

For $t$ weeks number of apps sold = $4200t$

Therefore

  $Totalnumberofapps=numberofappssoldin weeksafterfirstweek+Numberofappssoldinfirstweek$

  $\Rightarrow A=4200t+3305$

Therefore

Equation that represents the given situation is $A=4200t+3305$

b.

To determine

To find:How many weeks it will take for the company to sell $1,00,000$ apps.

Answer to Problem 61PPS

  $t=23.02$

Explanation of Solution

Given information:

Number of apps sold in the first week of availability = 3305

On average number of apps sold per hour = 25

  $A=1,00,000$

Equation that represents the given situation is $A=4200t+3305$

Substitute $A=1,00,000$

We get

  $\begin{array}{l}A=4200t+3305\\ \Rightarrow 1,00,000=4200t+3305\\ \Rightarrow 4200t=1,00,000-3305\\ \Rightarrow 4200t=96695\\ \Rightarrow t=\frac{96695}{4200}\\ \Rightarrow t=23.02\end{array}$

Number of weeks = $t=23.02$