Match each exponential function with its type and constant percent rate of change.(1 point)

Question

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y=270(0.5)0.7t
y=400(1.04)t2
y=42(1.67)t5
y=640(0.83)0.65t

Answer 1

To match each exponential function with its type and constant percent rate of change, we'll first analyze the forms of the given functions:

1. y = 270(0.5)^(0.7t) - This is a decay function since the base (0.5) is less than 1. The percent rate of change can be calculated as (0.5 - 1) * 100 = -50%. Thus, it has a -50% rate of change.

2. y = 400(1.04)^(t^2) - This is a growth function since the base (1.04) is greater than 1. The percent rate of change can be calculated as (1.04 - 1) * 100 = 4%. Thus, it has a 4% rate of change.

3. y = 42(1.67)^(t^5) - This is also a growth function since the base (1.67) is greater than 1. The percent rate of change can be calculated as (1.67 - 1) * 100 = 67%. Thus, it has a 67% rate of change.

4. y = 640(0.83)^(0.65t) - This is a decay function since the base (0.83) is less than 1. The percent rate of change can be calculated as (0.83 - 1) * 100 = -17%. Thus, it has a -17% rate of change.

Now, let's summarize the matching:

• y = 270(0.5)^(0.7t) → Decay, -50%
• y = 400(1.04)^(t^2) → Growth, 4%
• y = 42(1.67)^(t^5) → Growth, 67%
• y = 640(0.83)^(0.65t) → Decay, -17%

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