>>7926913
yes

multiply the number by itself every day.

>>7926925
in other words, x^2

>>7926925
>owe the bank a thousand dollars
>have a million the next day

>>7926935
>in other words, x^2

That's not "multiplying the number by itself every day." In fact that is slower than exponential ("compound interest").

>>7926935
You probably mean [eqn] x^t [/eqn]

>>7926913
>Is there a function where it would be faster to turn $1,000 into $100,000 than $1 into $100? What would it and its derivative look like?

There is an infinite number of such functions.

>>7926968
>mathfags try answering real questions

>it exists but I can't tell you how to find it

sounds like santa to me.

>>7926935
Dumbass, multiply a number by itself every single day is f (x)=a^(2^x) with a being your starting point

>>7926988
See>>7926995

>>7926988
>can't tell you how to find it

Ok faggot, exponential growth is

f(x) = a*e^(t*b), where a is initial value and b is some constant, yes? So how would you change that function to make it grow faster?

>>7926968
Surely you could provide a general form.

Would y' = y^2 fit OP's criteria?

>>7927033
There is no general form to /all/ of the functions that this holds true for.
Except, well...
f(t) so that if f' is the inverse of f then f'(100000) - f'(1000) < f'(1000) - f'(10)

>>7927355
Uhhh fucked up the numbers but my point stands

>>7926913
y = x + $99,000

>>7926925
>$1 multiplied by itself every day

>>7927603
what's wrong? You're having trouble with 1*1?

fucking americans.

Simple, the derivative if the derivitave is always positive. Lets say it's 2. then taking two antiderivatives, x^2+cx+k where c and k can be anything, including zero. Yeilding x^2 as such a function, where x is the distance between the two numbers of interest.

You're looking for a function that is superconvex, or logarithmically convex. This basically means the function grows faster than an exponential function. The factorial function is superconvex