Use induction to prove that 2? ? ? for any integer n> 0 . indicate type of induction used.
i proved the base case using n = 1, and for my induction hypothesis, i said that we assume n = k for 2^k > k, but i am stuck trying to get to n = k + 1.
so far i have:
2^k > k
2*2^k > 2*k
2^{k+1} > 2k

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)

Your company withheld $4,463 from your paycheck for taxes. you received a $713 tax refund. select the best answer round to the nearest 100 to estimate how much you paid in taxes.

Let x = a + bi and y = c + di and z = f + gi. which statements are true?