Determine if each of the following functions is a growth exponential or a decay exponential.

Question

a.
y equals 0.8 Superscript 2 x
b.
y equals 2 Superscript negative 1.8 x
c.
y equals 4 Superscript 0.4 x
d.
y equals 3 e Superscript negative 3 x
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Part 1
a. The function y equals 0.8 Superscript 2 x is a
▼
decay
growth
exponential.

Answer 1

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