How to solve the problem on the complexity of the algorithms below?

Question

Programming

Hello, help me decide:
Computer A is 100 times faster than computer B. If computer B processes n-th amount of input data in 1 hour with an algorithm with linear complexity, then how much data will computer A process in the same time if the complexity of the processing algorithm is:
a) Linear (n)
b) Quadratic (n^2)
c) Cubic (n^3)
d) Exponential (2^n)
Do I understand correctly:
a) 100n
b) 10n
c) Cubic root of 100n (4.64159n)
d )log(2)100n (6.644n)

Answer 1

d) incorrectly calculated.
Write an equation. Here you have a time function for n inputs f(n) on computer B. On computer A, the execution time will be - f(n)/100, because it is 100 times faster.
Now let x be the amount of data on computer A that needs to be found. Then you have f(x)/100 = f(n). Substitute the desired function for f() and find x. Spoiler, it will be similar, but not what you have in the question.