Answer :
To solve the problem of determining how much a baby will weigh after 1 year if it gains 10% in weight each month, we start by understanding the process of compounding growth.
1. Initial Weight: The baby weighs 7 pounds at birth.
2. Monthly Increase: Each month, the baby's weight increases by 10%. This means that at the end of each month, the baby's weight is 1.1 times its weight at the beginning of the month (since 1 + 0.10 = 1.1).
3. Time Period: We need to find out the baby's weight after 12 months, which is equivalent to 1 year.
4. Compounded Growth Calculation:
- At the end of the first month, the baby's weight will be 7 pounds 1.1.
- At the end of the second month, it will be (7 pounds 1.1) * 1.1, and so on.
- You keep multiplying by 1.1 for each month of growth.
5. Formula: The formula to calculate the compounded weight after a certain number of months is:
[tex]\[ \text{Final Weight} = \text{Initial Weight} \times (1 + \text{Monthly Rate})^{\text{Number of Months}} \][/tex]
Substituting the given values:
[tex]\[ \text{Final Weight} = 7 \times (1.1)^{12} \][/tex]
After evaluating this expression, the baby's weight at the end of one year is approximately 21.97 pounds.
Thus, the correct answer is 21.97 pounds.
1. Initial Weight: The baby weighs 7 pounds at birth.
2. Monthly Increase: Each month, the baby's weight increases by 10%. This means that at the end of each month, the baby's weight is 1.1 times its weight at the beginning of the month (since 1 + 0.10 = 1.1).
3. Time Period: We need to find out the baby's weight after 12 months, which is equivalent to 1 year.
4. Compounded Growth Calculation:
- At the end of the first month, the baby's weight will be 7 pounds 1.1.
- At the end of the second month, it will be (7 pounds 1.1) * 1.1, and so on.
- You keep multiplying by 1.1 for each month of growth.
5. Formula: The formula to calculate the compounded weight after a certain number of months is:
[tex]\[ \text{Final Weight} = \text{Initial Weight} \times (1 + \text{Monthly Rate})^{\text{Number of Months}} \][/tex]
Substituting the given values:
[tex]\[ \text{Final Weight} = 7 \times (1.1)^{12} \][/tex]
After evaluating this expression, the baby's weight at the end of one year is approximately 21.97 pounds.
Thus, the correct answer is 21.97 pounds.
