Final answer:
The Big Bang model is based on the idea that the universe began as a hot, dense state and has been expanding and cooling ever since. As the universe expanded and cooled, photons could settle into neutral atoms, allowing them to travel freely through space and reach us as the cosmic microwave background radiation.
Step-by-step explanation:
The statement that photons of the cosmic microwave background have traveled through space for almost 14 billion years follows from our model of the Big Bang, because the Big Bang model is based on the idea that the universe began as a hot, dense state and has been expanding and cooling ever since. As the universe expanded and cooled, it reached a point where electrons and photons could settle into neutral atoms, allowing photons to travel freely through space without interacting with matter. This is when the cosmic microwave background radiation was emitted, and these photons have been traveling through space for nearly 14 billion years, reaching us to this day.