Without defined values of a, b, and n, the equation is merely a formula and only informative as to the function.

Actually, that is the beauty of algebra. It describes mathematical functions in general terms without the restriction of defined values

We know that 2, 4, 8, 16, 32, 64,… is an exponential function
How that affects a steady growth rate of anything, is explained by Dr Albert Bartlett in his famous lecture on the “Exponential Function”

This is really important knowledge, and it is easy!

Something that excited me in The Science in Science Fiction by Lanford et al (1982) was about proving mathematically that nothing can go faster than the speed of light.

If you change the equations to faster than light you end up with the square root of minus one. -1

Of course there’s no such number, so you find yourself doing maths with imaginary numbers!

@rasilon
I can’t help but like you. I am a retired engineer (electrical). I am very happy with my career choice. Why? Because as an engineer I worked with engineers. Imagine the beauty in today’s political environment of working in a “bubble” of the population that uses logic, math, reason, and civil discourse to solve problems. Now, I’m not saying that there weren’t the fair amount of oddball religious or disturbed individuals you are bound to encounter in life, but in this “bubble” they were “handled” pretty swiftly.

I met lifelong friends who I both respect and enjoy being with. I married one of them. Admittedly, this is a sort of silo or echo chamber bubble, but I believe the world needs this particular echo chamber to thrive in order to succeed in a future that will present a multitude of challenges. Thoughts and prayers are woefully inadequate.

You may have noticed that this forum is very small and could actually benefit from some short-term exponential growth with persons like you. As a retired engineer, I can also tell you that it is one thing to understand a topic like exponential growth. It quite another to appreciate it.

Whatever career path you choose, be prepared for change! When I graduated in the top 10% of my class, an understanding of differential and integral calculus, differential equations, linear algebra, Laplace and Fourier transforms was sufficient. A few years later, an entirely new branch of mathematics became the basis for much computer science - that branch is Discrete mathematics.

Change is common to any field, so an important part of any education is the ability to learn. To enjoy learning! Best of luck to you, friend.

Cheerz
I suppose in any chosen field you’re bound to be with like-minded people. I keep off religion and politics, fatal to any discussion of anything. At best it just goes round in circles.

My “philosophy of philosophy” comes from what 1 of my teachers said to me; ideas in any sphere which are totally rejected and discredited by society often (not always, but often) contain at least some home truths

When I was on the Richard Dawkins Foundation website forums I managed to keep upsetting people about R&P, so they’re no-go areas for me now lol.

There’s alot more important things. 360 children are dying of starvation EVERY HOUR across the world and climate is changing

That’s what we have to focus on. That’s why we need to become a spacefaring species asap. When we’re terraforming and living on Mars and Venus, I think you’ll find problems on Earth will solve themselves

Thank you, @lausten
You’re absolutely right. My words clearly stated that an engineer/scientist cannot choose to ignore issues. If an engineer can’t make something work then (s)he will be unemployed. My posts very clearly stated kindness to @rasilon