Question

Suppose f(n) = 100n and g(n) = n 2 . Compute f(n)/g(n) for n = 1, 10, 100, 1000, and 10, 000.

Answer 1

f(1)/g(1) =100

f(10)/g(10) =10

f(100)/g(100) =1

f(1,000)/g(1,000) =0.1

f(10,000)/g(10,000) =0.01

Explanation:

Applying the values of n=1, 10, 100, 1,000, and 10,000. To the function f(n)/g(n) yields:

`f(n) = 100n\\g(n) = n^2\\\\(f(n))/(g(n)) =(100n)/(n^2)=(100)/(n)\\\\(f(1))/(g(1)) =(100)/(1)=100\\\\(f(10))/(g(10)) =(100)/(10)=10\\\\(f(100))/(g(1)) =(100)/(100)=1\\\\(f(1000))/(g(1000)) =(100)/(1000)=0.1\\\\(f(10000))/(g(10000)) =(100)/(10000)=0.01\\`