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Question 1177104: Seth found 50 plants before adding volunteers to the search, and the rate of increase is 12% per volunteer.
PART A
The function n that models the situation is n(x) = ____ (____)^x
For 0 ≤ x ≤ 5, the domain of the function is whole numbers from ____ to ___ The y-intercept is ____
PART B What is the average rate of change from 0 to 5 volunteers? Round to the nearest whole number_____-
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **PART A**
* **The function:** n(x) = 50(1.12)^x
* The initial number of plants is 50.
* The rate of increase is 12%, which means each volunteer adds 12% to the previous total. This is represented by multiplying by 1.12 (100% + 12% = 112% = 1.12).
* **Domain:** Whole numbers from 0 to 5
* The domain represents the number of volunteers, and you can't have a fraction of a volunteer.
* **y-intercept:** 50
* The y-intercept is the starting value when x (number of volunteers) is 0. This represents the initial number of plants Seth found himself.
**PART B**
To find the average rate of change from 0 to 5 volunteers, we'll use the function we found in Part A:
1. **Calculate n(0) and n(5):**
* n(0) = 50(1.12)^0 = 50
* n(5) = 50(1.12)^5 ≈ 88.12
2. **Find the difference in the number of plants:**
* n(5) - n(0) ≈ 88.12 - 50 = 38.12
3. **Divide by the change in the number of volunteers:**
* Average rate of change = 38.12 / (5 - 0) = 7.624
4. **Round to the nearest whole number:**
* Average rate of change ≈ 8
**Therefore, the average rate of change from 0 to 5 volunteers is approximately 8 plants per volunteer.**
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