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

Answer:

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

Step-by-step explanation:

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

$f(n) = 100n\\g(n) = n^2\\\\\frac{f(n)}{g(n)} =\frac{100n}{n^2}=\frac{100}{n}\\\\\frac{f(1)}{g(1)} =\frac{100}{1}=100\\\\\frac{f(10)}{g(10)} =\frac{100}{10}=10\\\\\frac{f(100)}{g(1)} =\frac{100}{100}=1\\\\\frac{f(1000)}{g(1000)} =\frac{100}{1000}=0.1\\\\\frac{f(10000)}{g(10000)} =\frac{100}{10000}=0.01$