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Kitty [74]
1 year ago
6

Taye recruits two people to be election campaign volunteers. The next week he ask each of those volunteers to recruit two more c

ampaign volunteers. He wants all new volunteers each week to recruit two more volunteers.
a. Determine a method to calculate the number of volunteers in any given week. Use that method to
calculate the number of volunteers recruited for each of the first 5 weeks.
b. Taye wants to recruit 150 volunteers by election day. During which week can some of the
volunteers stop recruiting new volunteers? Explain your reasoning.
Mathematics
1 answer:
jeka941 year ago
3 0

Using a geometric sequence, it is found that:

a) For the first 5 weeks, the numbers are: 2, 4, 8, 16, 32

b) Hence some of the volunteers can stop recruiting new volunteers during the 7th week.

<h3>What is a geometric sequence?</h3>

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

a_n = a_1q^{n-1}

In which a_1 is the first term.

For this problem, on the first week there are 2 people, and since each new people involve two more, the common ratio is of 2, hence the parameters for the geometric sequence are:

a_1 = 2, q = 2

Hence the number of people after n weeks is:

a_n = 2 \times 2^{n - 1}

For the first 5 weeks, the numbers are:

  • a_1 = 2 \times 2^{1 - 1} = 2
  • a_2 = 2 \times 2^{2 - 1} = 4
  • a_3 = 2 \times 2^{3 - 1} = 8
  • a_4 = 2 \times 2^{4 - 1} = 16
  • a_5 = 2 \times 2^{5 - 1} = 32

There will be 150 volunteers when a_n = 150, hence:

2 \times 2^{n - 1} = 150

2^{n-1} = 75

\frac{2^n}{2} = 75

2^n = 150

n = 7...

The above is because 2^7 = 128 and 2^8 = 256, and 128 < 150 < 256.

Hence some of the volunteers can stop recruiting new volunteers during the 7th week.

More can be learned about geometric sequences at brainly.com/question/11847927

#SPJ1

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