Get clear, concise, and accurate answers to your questions on IDNLearn.com. Our platform provides accurate, detailed responses to help you navigate any topic with ease.
Sagot :
Sure, let's carefully analyze the growth functions and match them to their appropriate verbal descriptions.
1. We have six functions:
- [tex]\( f_1(x) = 2.56(1.04)^x \)[/tex]
- [tex]\( f_2(x) = 256(1.4)^x \)[/tex]
- [tex]\( f_3(x) = 4(1.0256)^x \)[/tex]
- [tex]\( f_4(x) = 2.56(0.6)^x \)[/tex]
- [tex]\( f_5(x) = 4(1.256)^x \)[/tex]
- [tex]\( f_6(x) = 256(1.04)^x \)[/tex]
2. And three descriptions:
- Description A: The price of gas, which started at \[tex]$2.56 per gallon, increased at a rate of 4% per year. - Description B: The chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week. - Description C: A forest started with 256 maple trees, and the number of maple trees increased at a rate of 40% each year. ### Matching the Functions to Descriptions Description A: The price of gas, which started at \$[/tex]2.56 per gallon, increased at a rate of 4% per year.
- This describes exponential growth starting from \$2.56 with an increase rate of 4% per year.
- The function reflecting this situation is [tex]\( f(x) = 2.56 (1.04)^x \)[/tex].
Description B: The chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week.
- This describes exponential growth starting from 4 students with an increase rate of 2.56% per week.
- The function matching this description is [tex]\( f(x) = 4 (1.0256)^x \)[/tex].
Description C: A forest started with 256 maple trees, and the number of maple trees increased at a rate of 40% each year.
- This describes exponential growth starting from 256 trees with an increase rate of 40% per year.
- The function that fits this description is [tex]\( f(x) = 256 (1.4)^x \)[/tex].
### Summary
- Description A ("The price of gas... increased at a rate of 4% per year"): [tex]\( f(x) = 2.56 (1.04)^x \)[/tex]
- Description B ("The chess club... grew at a rate of 2.56% each week"): [tex]\( f(x) = 4 (1.0256)^x \)[/tex]
- Description C ("A forest... increased at a rate of 40% each year"): [tex]\( f(x) = 256 (1.4)^x \)[/tex]
In conclusion:
1. The function [tex]\( f(x) = 2.56 (1.04)^x \)[/tex] matches the description of the gas price.
2. The function [tex]\( f(x) = 4 (1.0256)^x \)[/tex] matches the description of the chess club membership.
3. The function [tex]\( f(x) = 256 (1.4)^x \)[/tex] matches the description of the forest's maple trees.
1. We have six functions:
- [tex]\( f_1(x) = 2.56(1.04)^x \)[/tex]
- [tex]\( f_2(x) = 256(1.4)^x \)[/tex]
- [tex]\( f_3(x) = 4(1.0256)^x \)[/tex]
- [tex]\( f_4(x) = 2.56(0.6)^x \)[/tex]
- [tex]\( f_5(x) = 4(1.256)^x \)[/tex]
- [tex]\( f_6(x) = 256(1.04)^x \)[/tex]
2. And three descriptions:
- Description A: The price of gas, which started at \[tex]$2.56 per gallon, increased at a rate of 4% per year. - Description B: The chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week. - Description C: A forest started with 256 maple trees, and the number of maple trees increased at a rate of 40% each year. ### Matching the Functions to Descriptions Description A: The price of gas, which started at \$[/tex]2.56 per gallon, increased at a rate of 4% per year.
- This describes exponential growth starting from \$2.56 with an increase rate of 4% per year.
- The function reflecting this situation is [tex]\( f(x) = 2.56 (1.04)^x \)[/tex].
Description B: The chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week.
- This describes exponential growth starting from 4 students with an increase rate of 2.56% per week.
- The function matching this description is [tex]\( f(x) = 4 (1.0256)^x \)[/tex].
Description C: A forest started with 256 maple trees, and the number of maple trees increased at a rate of 40% each year.
- This describes exponential growth starting from 256 trees with an increase rate of 40% per year.
- The function that fits this description is [tex]\( f(x) = 256 (1.4)^x \)[/tex].
### Summary
- Description A ("The price of gas... increased at a rate of 4% per year"): [tex]\( f(x) = 2.56 (1.04)^x \)[/tex]
- Description B ("The chess club... grew at a rate of 2.56% each week"): [tex]\( f(x) = 4 (1.0256)^x \)[/tex]
- Description C ("A forest... increased at a rate of 40% each year"): [tex]\( f(x) = 256 (1.4)^x \)[/tex]
In conclusion:
1. The function [tex]\( f(x) = 2.56 (1.04)^x \)[/tex] matches the description of the gas price.
2. The function [tex]\( f(x) = 4 (1.0256)^x \)[/tex] matches the description of the chess club membership.
3. The function [tex]\( f(x) = 256 (1.4)^x \)[/tex] matches the description of the forest's maple trees.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.
