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.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

answer: idk

step-by-step explanation: