Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

UpStudy AI · Accepted Answer

To determine whether an exponential function represents growth or decay, and to find the percentage rate of increase or decrease, we typically look at the function in the form:

$$ f(t) = a \cdot b^t $$

where:
- $$ a $$ is the initial value,
- $$ b $$ is the base of the exponential function,
- $$ t $$ is time.

1. **Identify Growth or Decay**:
   - If $$ b > 1 $$, the function represents exponential growth.
   - If $$ 0 < b < 1 $$, the function represents exponential decay.

2. **Determine the Percentage Rate**:
   - The percentage rate of increase or decrease can be calculated using the formula:
     - For growth: $$ \text{Rate} = (b - 1) \times 100\% $$
     - For decay: $$ \text{Rate} = (1 - b) \times 100\% $$

If you provide the specific exponential function you are working with, I can help you analyze it further!
To determine if an exponential function represents growth or decay, check if the base $$ b $$ is greater than 1 for growth or between 0 and 1 for decay. The percentage rate is calculated as $$ (b - 1) \times 100\% $$ for growth and $$ (1 - b) \times 100\% $$ for decay.

Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.

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