I may be ignorant, but 3% yearly growth doesn't strike me as exponential, rather steady. Exponential grows in factors, no? As in 3% this year, 9 % next year, 27% the year after, etc.
It is an exponential function if you express the final according to time in relation to the original, but the growth rate is not itself exponential. A matter of semantics.
Reductively, the function is f(t) = (1.03)^t - which is an exponential function.
3% per year, every year is compound growth. At his rate, it takes about 23 years for the economy to double. It doesn't take many doubling periods before things get out of hand. Many times it grows more than that in a year. I linked an old youtube in a comment below that explains logarhythmic and exponential growth.
Yeah I understand now. Exponential just over a longer time span than if the domain/input itself had an actual exponent. I realized it can still be exponential growth without an exponent.
Exponential functions of time share one characteristic: the growth rate is proportional to the current value. Anyone who’s studied differential equations can tell you that exponential functions are synonymous with that statement.
You would be right if interest wasn’t compounded. If we only earned interest on what we initially put in, our money would grow linearly, not exponentially, because we’re not earning interest on our interest payments. But with compound interest, the amount our money grows is equal to some constant (the interest rate) times the total amount of money in our account, previous interest payments and all. Growth rate is proportional to the present amount. That’s
exponential, and eventually it will grow out of control. Though, if you were to calculate how long it would take, you’d realize you’d be long dead thanks to the incredibly slow start.
I may be ignorant, but 3% yearly growth doesn't strike me as exponential, rather steady. Exponential grows in factors, no? As in 3% this year, 9 % next year, 27% the year after, etc.
It is an exponential function if you express the final according to time in relation to the original, but the growth rate is not itself exponential. A matter of semantics.
Reductively, the function is f(t) = (1.03)^t - which is an exponential function.
True, just a lot slower than f(t)=1.03t^2 so it's a slower burn.
3% per year, every year is compound growth. At his rate, it takes about 23 years for the economy to double. It doesn't take many doubling periods before things get out of hand. Many times it grows more than that in a year. I linked an old youtube in a comment below that explains logarhythmic and exponential growth.
Yeah I understand now. Exponential just over a longer time span than if the domain/input itself had an actual exponent. I realized it can still be exponential growth without an exponent.
Exponential functions of time share one characteristic: the growth rate is proportional to the current value. Anyone who’s studied differential equations can tell you that exponential functions are synonymous with that statement.
You would be right if interest wasn’t compounded. If we only earned interest on what we initially put in, our money would grow linearly, not exponentially, because we’re not earning interest on our interest payments. But with compound interest, the amount our money grows is equal to some constant (the interest rate) times the total amount of money in our account, previous interest payments and all. Growth rate is proportional to the present amount. That’s exponential, and eventually it will grow out of control. Though, if you were to calculate how long it would take, you’d realize you’d be long dead thanks to the incredibly slow start.
That makes a lot of sense, actually.