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.
