Mathematics

Problem

Let

f(x)=5x+2

g(x)=x^{2}+2x+1

and

h(x)=2^{x}

for all real

x\ge 0

. Answer the following. a. (i) Find

f(0)

g(0)

and

h(0)

. b. (ii) Without direct calculation of numerical values, arrange

f(6)

g(6)

and

h(6)

in ascending order. Give a clear justification for each comparison you make. c. (iii) Determine the least positive integer

n

for which

h(n)>g(n)>f(n)

. Show all steps in your reasoning.