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Let P(t) be a deer population (in thousands) of an ecological region t years after 2000. a graph of the derivative P(t) is given below. Use it to answer the following questions. help on question 6 a-f please

Let P(t) be a deer population (in thousands) of an ecological region t years after 2000. a graph of the derivative P(t) is given below. Use it to answer the following questions. help on question 6 a-f please

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let P(t) be a deer population (in thousands) of an ecological region t years after 2000. a graph of the derivative P(t) is given below. Use it to answer the following questions.

help on question 6 a-f please

**Question:** Let \( P(t) \) be a deer population (in thousands) of an ecological region, \( t \) years after 2000. A graph of the derivative \( P'(t) \) is given below. Use it to answer the following questions. **Graph Analysis:** - The graph is a line chart showing the derivative \( P'(t) \), which represents the rate of change in the deer population over time. - The \( x \)-axis is labeled \( t \) and represents the years after 2000. - The \( y \)-axis is labeled \( P'(t) \) and represents the rate of change in thousands of deer per year. - The plotted line begins at \( t = 2 \) with \( P'(t) = 2 \), increases to a peak at \( t = 4 \) with \( P'(t) = 6 \), decreases to \( P'(t) = 0 \) at \( t = 6 \), drops further to \( P'(t) = -2 \) at \( t = 10 \), and finally rises back to \( P'(t) = 2 \) at \( t = 12 \) and \( t = 14 \). **Questions:** (a) Calculate \( P'(8) \) and interpret this in terms of the deer population. (b) Indicate the years during which the deer population declined.
Transcribed Image Text:**Question:** Let \( P(t) \) be a deer population (in thousands) of an ecological region, \( t \) years after 2000. A graph of the derivative \( P'(t) \) is given below. Use it to answer the following questions. **Graph Analysis:** - The graph is a line chart showing the derivative \( P'(t) \), which represents the rate of change in the deer population over time. - The \( x \)-axis is labeled \( t \) and represents the years after 2000. - The \( y \)-axis is labeled \( P'(t) \) and represents the rate of change in thousands of deer per year. - The plotted line begins at \( t = 2 \) with \( P'(t) = 2 \), increases to a peak at \( t = 4 \) with \( P'(t) = 6 \), decreases to \( P'(t) = 0 \) at \( t = 6 \), drops further to \( P'(t) = -2 \) at \( t = 10 \), and finally rises back to \( P'(t) = 2 \) at \( t = 12 \) and \( t = 14 \). **Questions:** (a) Calculate \( P'(8) \) and interpret this in terms of the deer population. (b) Indicate the years during which the deer population declined.
**Math 140 - Written Homework 6: 3.1-3.2** **Page 3 of 3** **(c)** Order the following from least to greatest; do not need to find the values themselves. If there is a tie, indicate that with an equal sign. You \( P(0), P(2), P(3), P(5), P(7), P(9) \). **(d)** Order the following from least to greatest; do not need to find the values themselves. If there is a tie, indicate that with an equal sign. You \( P(1), P(3), P(6), P(7), P(9), P(10) \). **(e)** Order the following from least to greatest; do not need to find the values themselves. If there is a tie, indicate that with an equal sign. You \( P(0), P(2), P(3), P(5), P(7), P(9) \). **(f)** Evaluate the limit: \[ \lim_{{h \to 0}} \frac{{P(2+h) - P(2)}}{h} \]
Transcribed Image Text:**Math 140 - Written Homework 6: 3.1-3.2** **Page 3 of 3** **(c)** Order the following from least to greatest; do not need to find the values themselves. If there is a tie, indicate that with an equal sign. You \( P(0), P(2), P(3), P(5), P(7), P(9) \). **(d)** Order the following from least to greatest; do not need to find the values themselves. If there is a tie, indicate that with an equal sign. You \( P(1), P(3), P(6), P(7), P(9), P(10) \). **(e)** Order the following from least to greatest; do not need to find the values themselves. If there is a tie, indicate that with an equal sign. You \( P(0), P(2), P(3), P(5), P(7), P(9) \). **(f)** Evaluate the limit: \[ \lim_{{h \to 0}} \frac{{P(2+h) - P(2)}}{h} \]
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