Comments on: How To Think With Exponents And Logarithms

By: kalid

kalid — Sun, 21 Mar 2021 18:31:37 +0000

Hi Sven,

In this case, your usage is modeled by a linear (not exponential) change, which worked out to an average of 3.92 gallons a day. This happens to be about 1.92% of your starting amount.

If your usage was truly based on a percentage of 1.92% per day, that means when you had 100 gallons left, you would use 1.92 gallons that day. And when you have 50 gallons left, you'd only be using 50 * 1.92% = .96 gallons. (The less gallons you have, the less gallons you use.) But for something like heating, your usage was probably the same (3.92 gallons/day) no matter how many gallons you had left.

It's good to distinguish which situations have truly exponential behavior, where the usage is calculated against the current amount. (For example, radioactive materials -- they never truly decay, they just get smaller and smaller as they lose a fixed percentage of their current amount.)

By: Sven Leroux

Sven Leroux — Sat, 20 Mar 2021 04:52:36 +0000

So, I heat my house with propane. On day one, I started with 198 gallons. On day 51, I was empty. My daily usage averaged 3.92 gallons, thus 1.96% per day. However, if I calc using exponential decay, the result is 72 gallons remaining on day 51{198x(1-.0196)^51}. What am I missing to have such a discrepancy?

By: Sreekanth

Sreekanth — Wed, 15 Apr 2020 06:40:17 +0000

Hi Kalid, i feel this is called real understanding(mapping the mathematical equations to realtime world). I really appreciate your passion and efforts. I have a question which may look silly but as many say no question is silly.
You mentioned
logarithm of change -> cause of growth.
Why u considered change = finalvalue/intial value(ln(14.4/9.9)) Rather we generally see change = final value- intial value ln(14.4 - 9.9) or Change ratio = (final value- intial value)/intial value.
Eg: a change from 100 to 125 means
Change = 125-100=25
Change ratio = (125-100)/100= 1/4
Percentage change = 25%.
Please either correct me if am wrong or consider updating the aricle.
Thanks in advance.

By: kalid

kalid — Fri, 19 Apr 2019 04:07:41 +0000

In reply to Toshko Postalkov.

Hi Toshko, thanks for the note!

3.74% is the *instantaneous, continuous* growth rate during the 10-year period, found by ln(14.4 / 9.9) / 10.

3.81% is the *discrete annual* growth rate during the 10-year period, found by (14.4/9.9)^(1/10).

Hope that helps!