Question

18 During Covid-19 pandemic,many pharmaceutical companies escalated their research
work in order to provide the vaccine as early as possible in the research laboratory of
a company, the researchers noticed that the number of corona virus in a certain culture
doubles every hour. Assume that there were 30 viruses present in the culture originally.
Based on the above information, answer the following:
(1) Considering the number of viruses in the culture, the situation given above forms
(a) arithmetic progression (b) geometric progression
(c) arithmetic-geometric progression (d) no pattern observed, so none of above
(ii) If a progression is formed, refer to (i), then what will be the value of first term of this
progression ?
(a) o (b) 120 (c) 30 (d) 60
(iii) How many viruses will be present at the end of th hour ?
(a) (30)(2)" (b) (30)(2)-1 (c) (30)"(2) (d) (30)(2) +1
(iv) What will be the number of viruses at the end of 4th hour?
(a) 240 (b) (60)(2) (c) (30)(2) (d) (30)(2)
(v) How many viruses will be present at the beginning of 7th hour?
(a) 960 (b) 1160 (c) 1920 (d) 3840
(30) 72) (4-1).
3.
DANT​

Answer 1

Concept:

When one term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence. It is symbolised by:

a, a²,a³, and so forth.

where r is the common ratio and an is the first term.

It should be noticed that if we divide one word by its predecessor, the resulting number is the common ratio.

By dividing the third term by the second term, we obtain:

ar²/ar = r

In a similar vein:

ar³/ar² = r

ar²/ar³ = r

Given:

During Covid-19 pandemic,many pharmaceutical companies escalated their research

work in order to provide the vaccine as early as possible in the research laboratory of

a company, the researchers noticed that the number of corona virus in a certain culture

doubles every hour. Assume that there were 30 viruses present in the culture originally.

Find:

(1) Considering the number of viruses in the culture, the situation given above forms

(a) arithmetic progression (b) geometric progression

(c) arithmetic-geometric progression (d) no pattern observed, so none of above

(ii) If a progression is formed, refer to (i), then what will be the value of first term of this

progression ?

(a) o (b) 120 (c) 30 (d) 60

(iii) How many viruses will be present at the end of th hour ?

(a) (30)(2)" (b) (30)(2)-1 (c) (30)"(2) (d) (30)(2) +1

(iv) What will be the number of viruses at the end of 4th hour?

(a) 240 (b) (60)(2) (c) (30)(2) (d) (30)(2)

(v) How many viruses will be present at the beginning of 7th hour?

(a) 960 (b) 1160 (c) 1920 (d) 3840

Solution:

1)Since the virus doubles every hour,

It means r=2

Geometric progression.

2) a= 30

3)End of  hour, means second term

a=30

r=2

a₂=arⁿ⁻¹

    = 30 (2)²⁻¹

    = 30(2)

4)End of 4th hour means 5th term

  a₅=ar⁵⁻¹

       = 30(2)⁴

       = 480

5) Beginning of the 7th hour means 7th term

 a₇=ar⁷⁻¹

     = 30(2)⁶

       =1920

Therefore, the answers are geometric progression, (ii) 30 (iii)  30(2) (iv) 480 (v) 1920

#SPJ2

Answer 2

Answer:

(i)  (b) Geometric progression.

(ii)  (c) 30

(iii)  (c) (30)(2)

(iv) 480

(v) (c) 1920

Step-by-step explanation:

Given that

• During Covid-19 pandemic, many pharmaceutical companies escalated their research work in order to provide the vaccine as early as possible in the research laboratory of a company.
• The researchers noticed that the number of corona virus in a certain culture doubles every hour.
• Assume that there were 30 viruses present in the culture originally.

To find

(i) Considering the number of viruses in the culture, the situation given above forms

        (a) arithmetic progression

        (b) geometric progression

        (c) arithmetic-geometric progression

        (d) no pattern observed, so none of above

(ii) If a progression is formed, refer to (i), then what will be the value of first term of this progression ?

           (a) o (b) 120 (c) 30 (d) 60

(iii) How many viruses will be present at the end of the hour ?

          (a) (30)(2)" (b) (30)(2)-1 (c) (30)"(2) (d) (30)(2) +1

(iv) What will be the number of viruses at the end of 4th hour?

         (a) 240 (b) (60)(2) (c) (30)(2) (d) (30)(2)

(v) How many viruses will be present at the beginning of 7th hour?

        (a) 960 (b) 1160 (c) 1920 (d) 3840

Explanation

According the Question

We can say that,

(i) When we considering the number of viruses in the culture, the situation is forms in (b) geometric progression.

(ii) first term of this progression is (c) 30.

(iii) End of the hour means 2nd term.

      We have,

      First term a = 30, and

      Common ratio r = 2.

      We know that,

     nth term of GP

              $T_{n} = ar^{n-1}$

      Where,

            n = term number,

             r = Common ratio,

             a = First term,

       So, 2nd term of this GP.

              $T_{2} = ar^{2-1}$

                   = 30 ×$(2)^{2-1}$

                   = 30 × 2  

                   = 60

(iv) End of 4th hour, means 5th term,

     So,

              $T_{5} = ar^{5-1}$

                   = 30 ×$(2)^{5-1}$

                   = 30 ×$(2)^{4}$

                   = 30 × 16  

                   = 480

(iv) 7th hour, means 7th term,

     So,

              $T_{7} = ar^{7-1}$

                   = 30 ×$(2)^{7-1}$

                   = 30 ×$(2)^{6}$

                   = 30 × 64  

                  = 1920

So, the answers of this question.

(i)  (b) Geometric progression.

(ii)  (c) 30

(iii)  (c) (30)(2)

(iv) 480

(v) (c) 1920

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