Blessed Exponentially
Differential Equations: Growth Functions
"You have heard that it was said, 'Love your neighbor and hate your enemy.' But I tell you, love your enemies and pray for those who persecute you, that you may be children of your Father in heaven. He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous. If you love those who love you, what reward will you get? Are not even the tax collectors doing that? And if you greet only your own people, what are you doing more than others? Do not even pagans do that?”
"I will make you into a great nation, and I will bless you; I will make your name great, and you will be a blessing. I will bless those who bless you, and whoever curses you I will curse; and all peoples on earth will be blessed through you."
Elementary functions play an important role in calculus. The rate at which those elementary functions grow for increasing input values is one characteristic we study. [Note: Applications of this growth analysis appear in algorithm complexity analysis in computer science. Exponential growth is "bad" in this instance.] The fastest growing elementary function class is the exponential function; a function which takes various powers of a fixed numerical base. The principle of exponential growth is exploited in savings plans (save early and often!) and modeled in growth of bacteria.
Christ tells us in Matthew 5:43-47 that we are to love our neighbors AND our enemies. We also read in Genesis 12:2-3 that God blessed Abraham so that "all peoples on earth will be blessed through you." Together the concepts of exponential growth and "blessed to be a blessing" tell us to "pay it forward," so that God's love for humankind and goodness can grow exponentially.
