Does a man's penis continue to grow throughout his life?
No. Just as you will reach your adult height and grow no further, your penis will reach its adult size as determined by your genes and then cease to grow.
There are thousands of companies selling fraudulent medicines and surgeries claiming to make a man's penis grow larger. All they are selling are lies: lies that some men run after on the hope that they may be true. They are simply scams designed to take the money of the foolish and naive.
What makes people susceptible to such lies is their dissatisfaction with truth. It happens in the church (see II Thessalonians 2:8-12), and it should not surprise anyone that it happens in the world. If there is something people want to believe, there will be someone willing to tell them it is true. "For the time will come when they will not endure sound doctrine, but according to their own desires, because they have itching ears, they will heap up for themselves teachers; and they will turn their ears away from the truth, and be turned aside to fables" (II Timothy 4:3-4).
Perhaps the most amazing thing is that sexual satisfaction has nothing to do with the size of your penis. A wife's reproductive organs are designed to adjust to the size of her husband's penis. In fact, women report that a large penis is harder to adjust to than an average or small size penis. It is how the penis is used that makes a difference to a woman, not its size.
"Therefore I say to you, do not worry about your life, what you will eat or what you will drink; nor about your body, what you will put on. Is not life more than food and the body more than clothing? Look at the birds of the air, for they neither sow nor reap nor gather into barns; yet your heavenly Father feeds them. Are you not of more value than they? Which of you by worrying can add one cubit to his stature? So why do you worry about clothing? Consider the lilies of the field, how they grow: they neither toil nor spin; and yet I say to you that even Solomon in all his glory was not arrayed like one of these. Now if God so clothes the grass of the field, which today is, and tomorrow is thrown into the oven, will He not much more clothe you, O you of little faith?" (Matthew 6:25-30).