Which explicit formula can be used to model the same sequence? f(x) = 12(4)x f(x) = 3(4)x − 1 f(x) = 4(12)x f(x) = 4(3)x − 1

B. gives the required expression.

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Sebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12. Choose the explicit formula that can be used to model the same sequence.

A.) f(x) = 12(4)x

B.) f(x) = 3(4)x − 1

C.) f(x) = 4(12)x

D.) f(x) = 4(3)x − 1

Given the recursive formula f(x+1) = 4f(x) and second term is 12 then f(2) = 12

If x =2

f(2+1) =4f(2)

f(3)= 4f(2)

f(3)= 4*12

f(3) = 48

if x = 3

f(3+1) =4f(3)

f(4)= 4f(3)

f(4)= 4*48

f(4) = 192

To get the first term, we will substitute x = 1 into the recursive function;

f(1+1) =4f(1)

f(2) = 4f(1)

since f(2) = 12 then f(2) = 4f(1) = 12

f(1) = 12/4 = 3

The sequence formed by the first four terms of recursive function is 3, 12, 48, 192... which gives a geometric sequence.

The xth term of a geometric sequence is expressed as where a is the first term and r is the common ratio.

from the sequence above a is 3 and r = 12/3 = 48/12 = 194/48 = 4

Substituting this value into the nth term of the sequence;

This gives the required expression.

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )

chemists are often responsible for designing a chemical reaction and analyzing the products obtained from it. one significant part of designing a chemical reaction is determining the amount of each reactant that is needed and the amount of each product that will be produced. in order to do so, chemists use stoichiometry, the quantitative relationships between reactants and products.