Why did president truman decided to use the atomic bomb on japan in 1945
?

Because even after Germany and most other axis powers were repressed, Japan continued to kill American soldiers, prompting Truman to end their war regime.

President Truman decided to use the bomb for many reasons. Having not knowledge about the existence of the bomb until his presidency, he saw it as a new weapon developed by the US and that should be used for that purpose. Secondly, Truman wanted to avoid an invasion of Japan because it would be extremely costly, difficult, and simply horrible. It also meant the loss of many more American lives since the Japanese attacks were so brutal. Truman hoped that the use of the bomb would and it's astonishing effects would be enough for Japan to surrender and they would not have to invade them. Lastly, Truman wanted to use it to show the soviets of it's power for post world war II policies. I personally believe that Truman did the right thing. It was evident in all the battles in the pacific that Japan was extremely stubborn and would do anything but admit defeat. Just taking over the underpopulated islands on the way to Japan was very difficult because of the Japanese's tireless efforts. I think that the only way to make them surrender was to scare them into a surrender. The back and forth combat wasn't completely useless but exhausting and would make the war last longer than needed.The Japanese were so focused on fighting and trying to harm us, that they trained their soldiers to die in the desperate kamikaze attacks. I really don't think that invading their homeland would lead to a surrender or end to the war. Not only would they not surrender, but many American lives would be lost in the process unnecessarily. The bomb was ready and functional.

Im pretty sure the answer is d.) is more densely populated.

Their solution was to tax the colonists.