Question

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