Before reading on, please review the article: What are the Assumptions of Radiometric Dating?
Suppose you walk into a room and see a man holding a knife and a potato, and he has a basket of peeled potatoes on a table next to him. When the second hand on the clock reaches “12,” the man starts to peel the potato. He finishes peeling the potato and puts it in a basket right when the clock hand has made a full revolution and arrived back at “12.” In other words, it took the man one full minute to peel the potato. He grabs another potato, peels it, and puts it into the basket. Again, this took one full minute. You see the basket and count 35 peeled potatoes. You assume that the man has been peeling potatoes for 35 minutes, and each potato took one minute to peel. Your assumption is reasonable, but it is correct?
There are several things you don’t know about the man and his potatoes. You do not know if he has always peeled the potatoes at the same rate. Maybe at first he was slower and it took two minutes to peel one potato, but once he got better, he was able to increase his rate to one minute each. Or, he could have been very fast at the beginning but is now slowing down because he is growing tired. Secondly, you do not know if the man has removed any of the peeled potatoes or added the ones he peeled to a pre-existing basket. This could show that he was peeling faster or slower. Thirdly, you do not know if there were any peeled potatoes in the basket before the man ever started.
In summary, you do not know: the peeling rate (rate of decay); if any potatoes have been added to or taken away from the basket (if atoms have been added to the fossil or leached out); or how many potatoes were in the basket to start with (the initial conditions). Similarly, scientists do not know if the decay rate of atoms in fossils or rocks has always been constant, they don’t know if any of the atoms have been added or removed, and they don’t know how much of the parent and daughter atoms were in the specimen at the very beginning when the fossil or rock was formed.
This example was from a very well written book about worldviews and evidences for a young earth: “The Young Earth” (2007) by John Morris.
Similarly, you could compare these assumptions to a candle. Supposed you walk into a room and see a lit candlestick. You cannot determine how long it has been burning because you don’t know how long the candle was prior to being lit or how fast it was burning prior to you entering the room (it could have had an accelerant). You can make assumptions but the truth about the candle’s past cannot be known, just as it is with radiometric dating.