Question
Henry earns $0.50 in interest from his savings account every year. Is this an example of a linear or exponential relationship?
Equation:
f(x)=1.5x 5
f(x)=2x+100 4 = 7
f(x)=0.5x 3
f(x)=100x 2
f(x)=100(0.5)^x
f(x)=100(0.98)^x
f(x)=100(1.5)^x
f(x)=100(2)^x
Equation:
f(x)=1.5x 5
f(x)=2x+100 4 = 7
f(x)=0.5x 3
f(x)=100x 2
f(x)=100(0.5)^x
f(x)=100(0.98)^x
f(x)=100(1.5)^x
f(x)=100(2)^x
Answers
GPT-4o mini
Henry earning $0.50 in interest every year is an example of a linear relationship because the interest earned increases by a constant amount (i.e., $0.50) each year.
In the equations you've listed, the following represent linear relationships:
1. **f(x) = 2x + 100** - This is a linear equation where `2` is the slope indicating a constant increase.
2. **f(x) = 0.5x + 3** - This is a linear equation where `0.5` is the slope.
3. **f(x) = 100x + 2** - This is also a linear equation.
The other equations represent exponential relationships, as they involve a variable in the exponent:
1. **f(x) = 100(0.5)^x** - Exponential decay.
2. **f(x) = 100(0.98)^x** - Exponential decay.
3. **f(x) = 100(1.5)^x** - Exponential growth.
4. **f(x) = 100(2)^x** - Exponential growth.
So, the correct conclusion is that the situation regarding Henry's annual interest is linear, and among the given equations, those that are linear are: **f(x) = 2x + 100**, **f(x) = 0.5x + 3**, and **f(x) = 100x + 2**.
In the equations you've listed, the following represent linear relationships:
1. **f(x) = 2x + 100** - This is a linear equation where `2` is the slope indicating a constant increase.
2. **f(x) = 0.5x + 3** - This is a linear equation where `0.5` is the slope.
3. **f(x) = 100x + 2** - This is also a linear equation.
The other equations represent exponential relationships, as they involve a variable in the exponent:
1. **f(x) = 100(0.5)^x** - Exponential decay.
2. **f(x) = 100(0.98)^x** - Exponential decay.
3. **f(x) = 100(1.5)^x** - Exponential growth.
4. **f(x) = 100(2)^x** - Exponential growth.
So, the correct conclusion is that the situation regarding Henry's annual interest is linear, and among the given equations, those that are linear are: **f(x) = 2x + 100**, **f(x) = 0.5x + 3**, and **f(x) = 100x + 2**.