The total spent on research and development by the federal government in the United States during 2002–2012 can be approximated by S(t) = 3.1 ln t + 22 billion dollars (2 ≤ t ≤ 12), where t is the year since 2000.† What was the total spent in 2006 (t = 6)? (Round your answer to the nearest whole number.) $ billion

28 billion dollars

Step-by-step explanation:

The total spent on research and development by the federal government in the United States during 2002–2012 can be approximated by

 billion dollars (2 ≤ t ≤ 12), where t is the year since 2000.

If t=6, that is, In the year 2006,

=28 billion dollars (To the nearest billion dollars)

In 2006, the federal government of the United States spent approximately $28 billion on research and development.

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week