Question

True or False...


There is some value x > 2 for which x^100 <1.01^x

Answer 1

yes

Answer 2

eventually exponential always beats out polynomial

Answer 3

I kinda don't get what the question is asking..

Answer 4

is there a number that makes \((1.01)^x\) greater that \(x^{100}\)

Answer 5

certainly not true if \(x=50\) because \((1.01)^{50}\) is less than \(50^{100}\)

Answer 6

the numbers that make it bigger will be very very large,

Answer 7

so 100 log x and x log 1.01

Answer 8

yeah why not? solve
\[x\log(1.01)>100\log(x)\]

Answer 9

\[\log(1.01)\] is a very very small number (close to zero) but is it positive
and since \(x\) grows much faster than \(\log(x)\) at some point \[x\log(1.01)\] will be greater than \(100\log(x)\)

Answer 10

so like a very large number? so maybe plug in 10^10 for x?