3 ms·
What's your definition of exponential? If I invest $1,000 at 5% annual return, I expect to have 1000 * (1.05)^n after n years. That fits my definition of expo
by AnimalMuppet 2y ago
What's your definition of exponential?
If I invest $1,000 at 5% annual return, I expect to have 1000 * (1.05)^n after n years. That fits my definition of exponential - time is an exponent in the formula.
- mystified5016 2y agoIt's really not a matter of interpretation. Geometric and exponential growth are well defined mathematical concepts. Geometric functions can have exponents. This does not imply the function is exponential. These are very different things. https://en.m.wikipedia.org/wiki/Exponential_growth https://en.m.wikipedia.org/wiki/Exponential_growth
- AnimalMuppet 2y agoThe page you cite gives the formula for exponential growth as: {\displaystyle x_{t}=x_{0}(1+r)^{t}} Um, right, let me translate that into something that can display here: x(t) = x(0) * (1+r)^t Well, if you look at the formula I gave for compound interest: x(t) is the value at time t, x(0) is the value at time 0, namely $1000, (1+r) is 1.05, and t = n, the number of years. So, from your own cited article, how is that not exponential? Or were you agreeing with me, and disagreeing with glitchc?
- glitchc 2y agoMy quibble was about geometrics vs exponential, but beyond the mathematical distinction of discreteness, they are equivalent, so I stand corrected on that front.