Ascientist has discovered an organism that produces five offspring exactly one hour after

7 answers
Question:

Ascientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. each replicated organism also replicates at the same rate. at hour one, there is one organism. at hour two, there are five more organisms. how many total organisms are there at hour seven? 2,801 19,531 19,607 97.655

Answers

B. 19,531

Step-by-step explanation:

The correct answer is option (2) 19,531

Step-by-step explanation:

Given Data;

a = 1 (first term)

r = 5 (five offspring)

n = 7 ( number of hours)

Using the formula of a geometric progression, we have

S₇ = [tex]\frac{a(r^{n} - 1) }{r -1}[/tex]

Substituting, we have

S₇ = [tex]\frac{1(5^{7} -1) }{5-1}[/tex]

S₇ = 78124/4

    = 19531

Therefore, there are 19531 number of organisms at hour seven.

Number of organism after 7 hours will be 19531

Step-by-step explanation:

A scientist discovered an organism that produces 5 offspring in one hour and goes on to live for 1 week without producing any additional offspring.

That means the geometrical sequence will be formed with the common ratio of 5.

Now we know sum of a geometric sequence is represented by

[tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex]

where a = first term of the sequence

r = common ratio

n = number of terms

We have to calculate the total number of organisms after 7 hours.

[tex]S_{7}=\frac{1(5^{7}-1)}{5-1}[/tex]

= [tex]\frac{(78125-1)}{5-1}[/tex]

= [tex]\frac{78124}{4}[/tex]

= 19531

Therefore, after 7 hours number of organism will be 19531.

Step-by-step explanation:

In hour one, there is 1 organism. In hour two, there are 5 more organisms.

∴ the number of organism in each hour would be:

1, 5, 25, 125,

The series is in a Geometrical Progression.

The Sum of first n terms of a Geometrical Progression.

Sₙ = a(rⁿ-1)/r-1

where,

a = first term = 1

r = common ratio = 5

n = 7

We put the values:

S = 1 (5⁷ -1)/ 5-1

5⁷ -1/4

78125-1/4

78124/4

=19531

∴ after 7 hours the  number of organisms will be 19531

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Step-by-step explanation:

In hour one, there is 1 organism. In hour two, there are 5 more organisms.

∴ the number of organism in each hour would be:

1, 5, 25, 125,

The series is in a Geometrical Progression.

The Sum of first n terms of a Geometrical Progression.

Sₙ = a(rⁿ-1)/r-1

where,

a = first term = 1

r = common ratio = 5

n = 7

We put the values:

S = 1 (5⁷ -1)/ 5-1

5⁷ -1/4

78125-1/4

78124/4

=19531

∴ after 7 hours the  number of organisms will be 19531

For similar questions check out

the diameter is 16 cm. are you a teacher?

step-by-step explanation:

[tex]What measures of the cylinder do 26 and 34 describe? 26 cm 34 cm radius and diameter radius and hei[/tex]

Ithink it’s b because it say 3 plastic rings and all the balls

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