Determine if the exponential function shows exponential growth or decay and find the rate at which is growing/decaying as a percent. Exponential Function >=3,500(1.12) A y=10,000 (0.90) y=5(1.025) y = 160(0.79) y=1,950(0.875) Growth (G) or Decay (D)? Rate (%) Result

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Growth or Decay? AND Percentage Rate...**

Determine if the exponential function shows exponential growth or decay and find the rate at which it is growing/decaying as a percent.

| Exponential Function      | Growth (G) or Decay (D)? | Rate (%) | Result |
|---------------------------|--------------------------|----------|--------|
| \( y = 3,500(1.12)^t \)   |                          |          |        |
| \( y = 10,000(0.90)^t \)  |                          |          |        |
| \( y = 5(1.025)^t \)      |                          |          |        |
| \( y = 160(0.79)^t \)     |                          |          |        |
| \( y = 1,950(0.875)^t \)  |                          |          |        |

**Graph Explanation:**

On the graph to the left, there are multiple curves depicting exponential functions. Each curve corresponds to one of the functions listed in the table. The red curve, for instance, represents a growth function where the base of the exponential expression is greater than 1, indicating an increase over time. Conversely, the green curve represents a decay function where the base is less than 1, showing a decrease over time. Each curve is plotted over a grid, showing changes as the value of \( t \) increases.

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Transcribed Image Text:**Growth or Decay? AND Percentage Rate...** Determine if the exponential function shows exponential growth or decay and find the rate at which it is growing/decaying as a percent. | Exponential Function | Growth (G) or Decay (D)? | Rate (%) | Result | |---------------------------|--------------------------|----------|--------| | \( y = 3,500(1.12)^t \) | | | | | \( y = 10,000(0.90)^t \) | | | | | \( y = 5(1.025)^t \) | | | | | \( y = 160(0.79)^t \) | | | | | \( y = 1,950(0.875)^t \) | | | | **Graph Explanation:** On the graph to the left, there are multiple curves depicting exponential functions. Each curve corresponds to one of the functions listed in the table. The red curve, for instance, represents a growth function where the base of the exponential expression is greater than 1, indicating an increase over time. Conversely, the green curve represents a decay function where the base is less than 1, showing a decrease over time. Each curve is plotted over a grid, showing changes as the value of \( t \) increases. **Action:** A "Try It" button invites learners to engage with the content, possibly clicking it to check their answers or receive hints.
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