Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Question:**
What rate is required to grow 100 to 10,000 in 10 years?
**Explanation:**
To solve the problem of determining the growth rate required for an investment or value to grow from 100 to 10,000 over a period of 10 years, we can use the formula for compound interest:
\[ A = P(1 + r)^n \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years.
In this scenario:
- \( A = 10,000 \)
- \( P = 100 \)
- \( n = 10 \)
We need to find \( r \):
1. Substitute the values into the formula:
\[ 10,000 = 100(1 + r)^{10} \]
2. Divide both sides by 100:
\[ 100 = (1 + r)^{10} \]
3. Take the 10th root of both sides to solve for \( 1 + r \):
\[ (1 + r) = 100^{1/10} \]
4. Calculate the 10th root of 100:
\[ (1 + r) \approx 1.5849 \]
5. Subtract 1 from both sides:
\[ r \approx 0.5849 \]
6. Convert decimal to percentage:
\[ r \approx 58.49\% \]
**Conclusion:**
The required annual growth rate to grow an amount from 100 to 10,000 in 10 years is approximately 58.49%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50ecada7-73ae-429a-bfd7-3c03fe93abe4%2F38dee9ee-8cd2-49b6-b533-9e609064f775%2Fr8o3d2_reoriented.jpeg&w=3840&q=75)
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