Question

Ashish plants a daffodil on his 9 th birthday. If the plant has one daffodil to
start with and the number of daffodils doubles every week then how many
daffodils will be there after x weeks?

Answer 1

Answer:

add 1 to 10 u will get ans

Step-by-step explanation:

hope it will and follow

Answer 2

Answer:

= $2^{x-1}$

Explanation:

Given:

• Number of daffodils in the first week = 1
• Number of daffodils doubles every week

To find:

The number of daffodils at the end of x number of weeks.

Proof:

According to the question,

• Number of Daffodils in the first week = 1

Therefore,

• Number of daffodils in the second week = 1 × 2 = $2^1$
• Number of daffodils in the third week = 2 × 2 = 2²
• Number of daffodils in the fourth week = 2 ×2 × 2 = 2³
• Number of daffodils in the fifth week = 2 × 2 × 2 × 2 = $2^4$

Thus, in this series, the power of 2 is increasing by 1 every week.

If we divide each consecutive degree of 2 as the number of weeks, by $2^1$we see that:

Number of daffodils:

• For first week = $2 ^{1-1} = 2^0 = 1$                        [  $\frac{a^m}{a^n} = a^{m-n}$ ]
• For second week = $2^{2-1}= 2^1 = 2$
• For third week = $2^{3-1} = 2^2= 4$
• For fourth week = $2^{4-1}= 2^3 = 8$

Thus, when the number of weeks = x

The number of daffodils = $\frac{2^x }{2^1}$

Hence, number of daffodils when the number of weeks = x

= $2 ^{x-1}$

Hope you got that.

Thank You.