Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

#1 2021-12-13 15:40:59

Hannibal lecter
Member Registered: 2016-02-11
Posts: 330

population can represented as a LinearFunction/exponential same time?

Hi, I found this question it's very strange in math the function can be linear and exponential in such a form

OR

this is very strange is this only happen in population problems? is anyone has a comment in this phenomenon Last edited by Hannibal lecter (2021-12-14 20:43:06)

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

#2 2021-12-13 22:15:43

Bob Registered: 2010-06-20
Posts: 9,358

Re: population can represented as a LinearFunction/exponential same time?

This is two separate, and different, questions.  When the population rises by 50 per year that's a steady (linear) rise. The slope or gradient is 50.  So an equation of the form P = 1000 + 50t fits.  If you plot the graph you'll see it goes up by 50 each year.

A 5% increase will result in an upwards curve.  This is because the rise depends on the previous year's amount so as the amount goes up so does the rise.

5% leads to a multiplier of 1.05.  So each year the population is is 1.05 times as big as the previous year.  So the equation this time is 1000(1.05^t).

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Offline