Question
Select the functions that represent an Exponential Growth. \( \begin{array}{l}y=8(4)^{x} \\ y=2\left(\frac{5}{7}\right)^{x} \\ y=0.2(1.4)^{x} \\ y=\frac{3}{4}(0.99)^{x} \\ y=\frac{1}{2}(1.01)^{x}\end{array} \)
Ask by Powell Adkins. in the United States
Feb 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The functions that represent exponential growth are:
- \( y = 8(4)^x \)
- \( y = 0.2(1.4)^x \)
- \( y = \frac{1}{2}(1.01)^x \)
Solution
An exponential function represents growth if its base is greater than 1. Let's check each function:
1. y = 8(4)^x → Base = 4, which is greater than 1, so it represents exponential growth.
2. y = 2(5/7)^x → Base = 5/7 (approximately 0.714), which is less than 1; this represents exponential decay.
3. y = 0.2(1.4)^x → Base = 1.4, which is greater than 1, so it represents exponential growth.
4. y = (3/4)(0.99)^x → Base = 0.99, which is less than 1; this represents exponential decay.
5. y = (1/2)(1.01)^x → Base = 1.01, which is greater than 1, so it represents exponential growth.
Thus, the functions that represent exponential growth are:
• y = 8(4)^x
• y = 0.2(1.4)^x
• y = (1/2)(1.01)^x
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Simplify this solution The Deep Dive
Exponential growth functions have a base greater than 1. In your list, the functions that exhibit exponential growth are: 1. \( y=8(4)^{x} \) – Here, the base is 4, which is greater than 1, indicating rapid growth as \( x \) increases. 2. \( y=0.2(1.4)^{x} \) – This function has a base of 1.4, also above 1, reflecting a steady increase. The rest of the functions have bases less than or equal to 1, which would demonstrate either decay or constant results. Keep an eye out for those bases!
