Question

On mobile devices, global voice traffic has been growing by approximately 222 petabytes (\text{PB})(PB)left parenthesis, P, B, right parenthesis per month, while global data traffic has been growing by approximately 7\%7%7, percent per month. At the end of one month in 200720072007, each of the two traffic volumes equaled 110\,\text{PB}110PB110, space, P, B per month. What was the total expected traffic (data and voice combined) 444 months later? Round to the nearest \text{PB}PBP, B.

Answer 1

Answer:

Voice data consumed: 118PB

Global data consumed: 144PB

Step-by-step explanation:

At a given month voice and data trafic are equal at 110 PB each

Rewriting the info into formulae will give us

Voice_Data=Prev_VD+2PB*Month

[tex]\left \{ {{Global\_Data_{(M+1)}=Global\_Data_{(M)}*\left(1+0.07\right)} \atop Global\_Data_{(M+2)}=Global\_Data_{(M+1)}\left(1+0.07\rigt)=Global\_Data_{(M)}\left(1+0.07\right)^2} \right. \\  \\

It follows: Global\_Data_{(M+N)}=Global\_Data_{(M)}}\left(1+0.07\right)^N[\tex]

where we rewrite the percentage as a ratio (dividing by 100)

One grows at a constant rate,and the other grows at a rate that depends on the Data already consumed.

Knowing that at one point they are the same, we can use that value as Previous voice data and previous global data:

Voice_Data=110PB+2PB*Month

Global_Data=110PB*(1+0.07)**Month

To see what happens after 4 months, simply replace the Month value by 4 and evaluate: