69.1k views
3 votes
Nf(n)15210320440Recursive Function:Explicit Function:

User Ghassen
by
8.7k points

1 Answer

1 vote

You have the following data set:

n | f(n)

1 5

2 10

3 20

4 40

In order to determine the resurve function associated to f(n), you consider that each term of f(n) is twice the previous one. Thus you have:

f(n) = 2*f(n-1) "this is the recursive function"

The explicit function is obtained by coinsider the values of n letf side of the table. You can notice that f(n) is multiple of products of 2's, that is:

f(n) = 5(2)ⁿ⁻¹ "this is the explicit function"

In fact, you obtain for the values of n:

f(1) = 5(2)¹⁻¹ = 5(2)⁰ = 5(1) = 5

f(2) = 5(2)²⁻¹ = 5(2)¹ = 5(2) = 10

f(3) = 5(2)³⁻¹ = 5(2)² = 5(4) = 20

f(4) = 5(2)⁴⁻¹ = 5(2)³ = 5(8) = 40

which coincides perfectly with the results of the table

User Demonofthemist
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.