Get expert advice and insights on any topic with IDNLearn.com. Our experts provide timely and precise responses to help you understand and solve any issue you face.
Sagot :
To solve this problem, let's carefully evaluate both Pierre's and Scott's equations based on the given conditions.
We need to write an exponential growth equation that has:
- A starting value of 300
- A growth rate of 2%
### Evaluation of Pierre's Equation:
Pierre suggests the equation:
[tex]\[ y = 300(1.02)^x \][/tex]
Let's break this down:
1. The initial value is 300, which matches the problem statement.
2. The growth rate is 2%. To convert a percentage to a decimal, we divide by 100:
[tex]\[ 2\% = \frac{2}{100} = 0.02 \][/tex]
3. An exponential growth formula typically looks like:
[tex]\[ y = \text{initial value} \times (1 + \text{growth rate as a decimal})^x \][/tex]
4. Therefore, the growth rate as a base should be:
[tex]\[ 1 + 0.02 = 1.02 \][/tex]
Pierre's equation matches this form perfectly:
[tex]\[ y = 300(1.02)^x \][/tex]
Hence, Pierre's equation correctly represents the given conditions, and Pierre is right.
### Evaluation of Scott's Equation:
Scott suggests the equation:
[tex]\[ y = 300(1.2)^x \][/tex]
Let's analyze this:
1. The initial value is 300, which again matches the problem statement.
2. According to Scott, the base of the exponent is 1.2.
3. However, the correct base should be:
[tex]\[ 1 + \text{growth rate as a decimal} = 1 + 0.02 = 1.02 \][/tex]
Scott's base of 1.2 does not match the 1.02 required for a 2% growth rate. Therefore, Scott's equation does not accurately represent the given conditions, and Scott is incorrect.
### Conclusion:
- Pierre is right. His equation correctly accounts for a 2% growth rate by using the base 1.02.
- Scott is incorrect because his base of 1.2 does not represent a 2% growth rate.
So, the correct evaluation is as follows:
a. Pierre is right. \( 2\% \) written as a decimal is \( 0.02 \), so the base should be \( 1 + 0.02 = 1.02 \). Hence, Pierre's equation:
[tex]\[ y = 300(1.02)^x \][/tex]
correctly represents the problem.
Scott's equation does not reflect the correct growth rate and thus is:
[tex]\[ y = 300(1.2)^x \][/tex]
incorrect for a 2% growth rate.
We need to write an exponential growth equation that has:
- A starting value of 300
- A growth rate of 2%
### Evaluation of Pierre's Equation:
Pierre suggests the equation:
[tex]\[ y = 300(1.02)^x \][/tex]
Let's break this down:
1. The initial value is 300, which matches the problem statement.
2. The growth rate is 2%. To convert a percentage to a decimal, we divide by 100:
[tex]\[ 2\% = \frac{2}{100} = 0.02 \][/tex]
3. An exponential growth formula typically looks like:
[tex]\[ y = \text{initial value} \times (1 + \text{growth rate as a decimal})^x \][/tex]
4. Therefore, the growth rate as a base should be:
[tex]\[ 1 + 0.02 = 1.02 \][/tex]
Pierre's equation matches this form perfectly:
[tex]\[ y = 300(1.02)^x \][/tex]
Hence, Pierre's equation correctly represents the given conditions, and Pierre is right.
### Evaluation of Scott's Equation:
Scott suggests the equation:
[tex]\[ y = 300(1.2)^x \][/tex]
Let's analyze this:
1. The initial value is 300, which again matches the problem statement.
2. According to Scott, the base of the exponent is 1.2.
3. However, the correct base should be:
[tex]\[ 1 + \text{growth rate as a decimal} = 1 + 0.02 = 1.02 \][/tex]
Scott's base of 1.2 does not match the 1.02 required for a 2% growth rate. Therefore, Scott's equation does not accurately represent the given conditions, and Scott is incorrect.
### Conclusion:
- Pierre is right. His equation correctly accounts for a 2% growth rate by using the base 1.02.
- Scott is incorrect because his base of 1.2 does not represent a 2% growth rate.
So, the correct evaluation is as follows:
a. Pierre is right. \( 2\% \) written as a decimal is \( 0.02 \), so the base should be \( 1 + 0.02 = 1.02 \). Hence, Pierre's equation:
[tex]\[ y = 300(1.02)^x \][/tex]
correctly represents the problem.
Scott's equation does not reflect the correct growth rate and thus is:
[tex]\[ y = 300(1.2)^x \][/tex]
incorrect for a 2% growth rate.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.