Solved:
Answered by AI, Verified by Human Experts
(0)
(0)Arrange the following five functions in order of increasing growth rate with g(n) following f(n) if and only if f(n) = O(g(n)).
A)in
B) 10n
C)n^{\frac{3}{2}}
D)2logen
E)n^{\frac{5}{3}}
Is the order:
a. A,D,C,E,B
b. A,C,D,E,B
c. E,D,C,A,B
d. E,A,D,C,B
Explain why.
The correct order is option (a) **A, D, C, E, B** where the functions'growth ratesare arranged in increasing order: **A < D < C < E < B**.The order of increasing growth rate can be determined bycomparingthe functions using Big O notation, which represents an upper bound on the growth rate of a function. In this case, we are looking for functions where f(n) = O(g(n)), meaning that f(n) grows at most as fast as g(n).Let's analyze the given functions:A) inB) 10nC) nD) 2E) nNow, let's compare these functions based on their growth rates:- **A) in**: This is a linear function.- **B) 10n**: This is also a linear function, but with a constant factor of 10.- **C) n**: This is a polynomial function with a power of 3/2.- **D) 2**: This function grows exponentially but with a base of 2 and a logarithmic exponent. The logarithmic exponent keeps the growth rate in check.- **E) n**: This is a polynomial function with a power of 5/3.Now, let's compare the functions in terms of their growth rates:- **A < B**: Linear growth is slower than linear growth with a constant factor.- **B < C**: Polynomial growth with a lower exponent is slower than polynomial growth with a higher exponent.- **D < B**: Exponential growth with a logarithmic exponent is slower than linear growth with a constant factor.- **D < E**: Exponential growth with alogarithmicexponent is slower than polynomial growth with a lower exponent.Based on these comparisons, the correct order of increasing growth rate is: **A, D, C, E, B**, which corresponds to option (a) **A,D,C,E,B**.Explanation:- **A < D**: Linear growth is slower than exponential growth with a logarithmic exponent.- **D < C**: Exponential growth with a logarithmic exponent is slower than polynomial growth.- **C < E**: Polynomial growth with a lower exponent is slower than polynomial growth with a higher exponent.- **E < B**: Polynomial growth with a higherexponentis slower than linear growth with a constant factor.Therefore, the correct answer is option (a) **A,D,C,E,B**.Learn more aboutgrowth ratesbrainly.com/question/13870574#SPJ11...