How can a phone transmit the signal back to tower?
I'm out of date on how modern mobile telephone networks handle multiple simultaneous voice calls but I believe each phone is allocated a time slot and there may be up to 100 time slots but it could be forty (something nagging in the back of my mind!). 

However it doesn't matter for answering this question; we can assume 100 time slots and that means the phone has to compress its outgoing voice message and transmit it in one hundredth of the time that the old fashioned analogue system had. That old system allocated a frequency for each handset and is now out-of-date.

Let's assume that the voice data could be compressed to 10 kbps and given that it has to be transmitted in one-hundredth the time it will need to store  data and transmit it at about 1 Mbps. Again, don't hang me on this if I'm not up to the latest 4G methods because that isn't important for this question I feel.

So, the tower receiver is handling a data rate of around 1 Mbps continuously to service up to 100 simultaneous voice calls. How much received power does the tower antenna need to adequately recover the data you would consider next.

The thermal noise per hertz for 50 ohms is -174 dBm and we wish to exceed this with sufficient margin to make data reception viable so, a well trodden formula says we need 100 times this power or -154 dBm. But that is "per Hz" and we need to have a bandwidth of about 1 MHz to adequately convert an RF signal carrying 1 Mbps data back to usable data. So the formula (at an ambient of 25 degC) becomes: -

Received power in dBm = -154 dBm + 10 log\$_{10}\$(data rate)

For the example of 1 MHz BW, we need a received signal in the order of -94 dBm. Given that RF engineers normally load this with a thing called fade margin (20 dB to 30 dB more) we would probably be OK statistically with -74 dBm.

Then there is link loss and the formula for free space is this:-

Link loss (dBm) = 32.45 + 20 loglog\$_{10}\$(Fc) + 20 log log\$_{10}\$(distance in km)

Fc is in MHz and is the carrier frequency. I'm going to assume that the telephone carrier frequency is about 2 GHz but don't hang me if I'm too far out.

If the distance is 3 km then the link loss is 32.45 dB + 66 dB +9.54 dBm. Overall that is about 108 dB lost between transmitter and receiver but we will have antenna gain and this could drop to maybe 102 dB or better.

We need -74 dBm therefore we need to transmit a level that is 102 dB higher or 28 dBm. 28 dBm is a power of 631 mW. Not a million miles from the 200 mW but the important thing is that you know have the fundamentals to put the real numbers into.