Question

I have a sort of general question regarding the exponential function (ab^t). I understand what each variable stands for, but I don't understand why it works.

For example:

a) 100 + (100 (.10)) = 110
b) 110 + (110 (.10)) = 121

Using ab^t saves you the trouble of going through step a, above.

100 (1.10)^2 = 121

I like the fact that it works, but I don't understand why it works. Why does raising ab to the t power always work? I have the formula memorized, but I just can't see why it works. Is there a proof of this out there somewhere or can someone explain why it works?

Thanks,

Okubow

Answer 1

it has to do with property of exponents
2^3 = 2*2*2
i could repeat this multiplication x times or i could say 2^x
from above example
100(1.1)^2 = 100(1.1*1.1)
this is same as doing 100*1.1 then multiplying by 1.1 again
Or multiply 1.1*1.1 first then multiply by 100
The key is i get the same answer no matter which order i do the multiplication
using exponents is just a short hand way of doing repeated multiplications
im sure there is some fancy mathematical proof out there
anyway thats the gist of it

Answer 2

Thanks, dumbcow. That's the kind of answer I was looking for.

This helped me to visualize it!:

100(1.1)^2 = 100(1.1*1.1)

Answer 3

good to hear
your welcome