Plant Growth Calculation: One Year Estimate
The problem asks for the height of a plant after one year, given its current height and a quarterly growth rate.
- Initial Height ($H_0$): 1 m
- Growth Rate per quarter: 10% or 0.10
- Time Period: 1 year = 4 quarters (since growth happens every 3 months)
Calculating Growth Over Four Periods
The growth is compounded quarterly. We can calculate the final height using the formula for compound growth:
$ H_{final} = H_0 \times (1 + \text{rate})^{\text{number of periods}} $
Substitute the known values:
$ H_{final} = 1 \, \text{m} \times (1 + 0.10)^4 $
$ H_{final} = 1 \, \text{m} \times (1.10)^4 $
Determining Final Height
Calculate the value of $(1.10)^4$:
- $(1.10)^2 = 1.21$
- $(1.10)^4 = (1.10)^2 \times (1.10)^2 = 1.21 \times 1.21 = 1.4641$
Therefore, the final height is:
$ H_{final} = 1 \, \text{m} \times 1.4641 = 1.4641 \, \text{m} $
The height after one year is 1.4641 m. This value is closest to 1.46 m.
Important Questions from Percentage (Notes)
In an election between two candidates, a candidate who got $30\%$ of the total votes is defeated by $15000$ votes. The number of votes obtained by the winning candidate is:-
- Which of the following multipliers will increase a given number by 25.3 % ?
If A earns \(33\frac{1}{3}%\) more than B, then how much percent does B earn less than A?
- दो उम्मीदवारों के बीच एक कॉलेज चुनाव में, एक उम्मीदवार को कुल वैध मतों में से $55\%$ वोट मिले । $15\%$ वोट अवैध थे । यदि कुल वोट $15,200$ थे, तो दूसरे उम्मीदवार को कितने वैध वोट मिले ?
- एक शहर की जनसंख्या एक दशक में $1,75,000$ से बढ़कर $2,62,500$ हो गई । प्रति वर्ष जनसंख्या में औसत प्रतिशत वृद्धि है
