The running time of an algorithms is $(2.2)^n$. I have to tell what is the maximum $n$ for reaching 1.000.000 steps.
What type of a function is $(2.2)^n$? How its output depends on the input $n$?
Thank you very much in advance for your help!
Best, Ina
$2.2^n$ is the same as $\frac{22^n}{100^n}$, this should tell you how it is calculated. We have the following inequality:
$2^n<2.2^n<3^n$. So it is exponential time, if your algorithm takes approximately $2.2^n$ operations then for an input of $25$ you need approximately $3\times 10^8$ operations, which is going to take a somewhere between half a second and half a minute. However, any input above $40$ will take more than a decade.