Question

a caterpillar grew twice the length compared to the previous day .if it measured 32 millimeter on 12 day on which day was the length of the caterpillar 14 millimeter ​

Answer 1

Answer:

32mm=12day

1mm=12/32

14mm=12/32×14

=7/4

=1.75

therefore approximately on the 1 st day it was 14mm

Answer 2

Let the initial length of the Caterpillar = x mm.

On second day, it's length would be = 2x

On third day it's length would be = 4x

On n th day, it's length would be = 2^(n-1)x.

Given, It was 32 millimeter on 12th day

⇒2^11 x = 32

⇒2^11 x = 2^5

⇒ 2^(11 - 5) = 1/x

⇒ 2^ 6 = 1/x

⇒ 2^ - 6 = x

Now length on n th day would be,

⇒2^(n-1) × 2^ - 6

⇒ 2^ ( n - 7)

So Length of the caterpillar is exponent of 2.

8 < 14 < 16

Therefore, If we find the day on which it's length was 16 mm, That day will be the required day. As the caterpillar grows from 8 to 16mm, It's length would have been 14 also.

⇒ 2^(n-7) = 16

⇒ 2^(n-7) = 2^4

⇒ n - 7 = 4

⇒ n = 4 + 7

⇒ n = 11.

So on 10th day it's length was 8 mm, and on 11 th day it's length was 16 mm. So during the 11 th day, It's length was 14 mm.