To determine whether each function is a growth or decay exponential, you can look at the base of the exponent:
- If the base is greater than 1, it represents exponential growth.
- If the base is between 0 and 1, it represents exponential decay.
- If the base is negative, additional information regarding the context is needed, but typically we consider real bases.
Let's analyze each function provided:
a. \( y = 0.8^{2x} \)
- The base is 0.8, which is less than 1.
- Conclusion: This is a decay exponential.
b. \( y = 2^{-1.8x} \)
- The base is \( 2 \), which is greater than 1, but since the exponent is negative (\(-1.8x\)), it represents decay.
- Conclusion: This is a decay exponential.
c. \( y = 4^{0.4x} \)
- The base is \( 4\), which is greater than 1.
- Conclusion: This is a growth exponential.
d. \( y = 3 e^{-3x} \)
- The base is \( e \approx 2.718\), which is greater than 1, but the exponent is negative (\(-3x\)), indicating decay as well.
- Conclusion: This is a decay exponential.
So, to summarize:
- a. Decay
- b. Decay
- c. Growth
- d. Decay