Free Response Question Rate of Change

1. Free Response QuestionRate of Change Individual Project by Rebeca Otero

2. The Question: For 0 t 31, the rate of change of the number of mosquitoes on Tropical Island at time t days is modeled by mosquitoes per day. There are 1000 mosquitoes on Tropical Island at time t=0. Show that the number of mosquitoes is increasing at time t=6. At time t=6, is the number of mosquitoes increasing at an increasing rate or increasing at a decreasing rate? Give reason to your answer. According to the model how many mosquitoes will be on the island at time t=31? Round your answer to the nearest whole number. To the nearest whole number, what is the maximum number of mosquitoes for 0 t 31? Show that the analysis that leads to your conclusion.

3. Part A: 4.438>0 so the number of mosquitoes is increasing at t=0.

4. Part B: The number of mosquitoes is increasing at a decreasing rate because R’(6)= -1.913 so R’(t)<0 at t=6.

5. Part C: R(t)=1000 when t=0: There are 964 mosquitoes on the Tropical Island at t=31.

6. Part D R(t)=0 when t=0,7.854, or 23.562 0<t<7.854 R(t) is positive 7.854<t<23.562 R(t) is negative 23.562<t<31 R(t) is positive The absolute minimum must occur at 7.854 or at 31 There are 964 mosquitoes at t=31 so the maximum number of mosquitoes occurs at t=7.856 with 1039 mosquitoes.

7. Citations • College board 2004 AP Free Response Questions: question #2 • Images from photobucket and google image searches so not exactly sure…… • Answers from my brain <3 and checked on answer sheet =D

8. The End!