03-19-2020, 08:58 PM
That’s linear growth with a slope of two. Exponential growth is like this example: 2,4,16, 256, 65536.....
Is it really? Are you sure you don't want to double check your answer? Maybe see what your neigbbor put down for this?
Linear growth is defined by a growth with a regular change each step. The equation is something like y=2x where the sequence would be
0, 2, 4, 6, 8... (+2 to the result each step, no difference to the rate of change)
Quadratic growth is defined by a parabolic increase in tbe rate of change. The math equation is like y=x^2 so the sequence would be:
0, 1, 4, 9, 16... (+2 to the rate change each step (1, 3, 5, 7...)
Exponential (or geometric growth under limited conditions) is defined when the rate of change is proportional to the value itself. The math is of the form y=2^x so the sequence would be:
1, 4, 8, 16, 32... (Not only are the values going up but the rate of change is also quickly going up (3, 4, 8, 16) ) The faster it goes the faster it increases in going)
Feel free to check my answers against the key:
https://en.m.wikipedia.org/wiki/Exponential_growth
What tricks most people is that the results after 5 steps seem pretty close, not really a big deal; however this fails to realize how quickly the differences in the growth rate happen. So after 20 steps;
Linear: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ... 40
Quadratic; 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ... 400
Exponential: 0, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 ... 1048576
As seen with the spreading of viruses, an exponential change each step quickly outraces the other forms of growth (and most people's ability to grasp the pattern and predict the future - 26, 52, 104, 208, 416, 832, 1664 cases in about 3 weeks)
I'm not sure exactly what the equation is for the example you gave (do you know?) - but it appears to be some aggressive exponenial like y=x^x^x which will grow extremely fast, but this isn't even required to overwhelm the system. A simple 1.15^x like we're seeing most days will reach the same result in short order.
As Newton invented/discovered the calculus (math about the rates of change) while on leave from Trinity College in Cambridge during London's Black Plague of 1665, I make this mathematical offering to the integral and differential gods of COVID-19 in the hope they either slow their roll or passover my humble and observant abode.
http://www.openculture.com/2020/03/isaac...-1665.html
Is it really? Are you sure you don't want to double check your answer? Maybe see what your neigbbor put down for this?
Linear growth is defined by a growth with a regular change each step. The equation is something like y=2x where the sequence would be
0, 2, 4, 6, 8... (+2 to the result each step, no difference to the rate of change)
Quadratic growth is defined by a parabolic increase in tbe rate of change. The math equation is like y=x^2 so the sequence would be:
0, 1, 4, 9, 16... (+2 to the rate change each step (1, 3, 5, 7...)
Exponential (or geometric growth under limited conditions) is defined when the rate of change is proportional to the value itself. The math is of the form y=2^x so the sequence would be:
1, 4, 8, 16, 32... (Not only are the values going up but the rate of change is also quickly going up (3, 4, 8, 16) ) The faster it goes the faster it increases in going)
Feel free to check my answers against the key:
https://en.m.wikipedia.org/wiki/Exponential_growth
What tricks most people is that the results after 5 steps seem pretty close, not really a big deal; however this fails to realize how quickly the differences in the growth rate happen. So after 20 steps;
Linear: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ... 40
Quadratic; 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ... 400
Exponential: 0, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 ... 1048576
As seen with the spreading of viruses, an exponential change each step quickly outraces the other forms of growth (and most people's ability to grasp the pattern and predict the future - 26, 52, 104, 208, 416, 832, 1664 cases in about 3 weeks)
I'm not sure exactly what the equation is for the example you gave (do you know?) - but it appears to be some aggressive exponenial like y=x^x^x which will grow extremely fast, but this isn't even required to overwhelm the system. A simple 1.15^x like we're seeing most days will reach the same result in short order.
As Newton invented/discovered the calculus (math about the rates of change) while on leave from Trinity College in Cambridge during London's Black Plague of 1665, I make this mathematical offering to the integral and differential gods of COVID-19 in the hope they either slow their roll or passover my humble and observant abode.
http://www.openculture.com/2020/03/isaac...-1665.html