The number of people who donated to a certain organization between 1975 and 1992 can be modeled by the equation donors,where t is the number of years after 1975.Find the inflection point(s)from through ,if any exist.
A) There are no inflection points from
B) There is one inflection point at
C) There are inflection points at
D) There is one inflection point at
E) There are inflection points at , ,

Question

The number of people who donated to a certain organization between 1975 and 1992 can be modeled by the equation  donors,where t is the number of years after 1975.Find the inflection point(s)from  through  ,if any exist. ​
A) There are no inflection points from 
B) There is one inflection point at 
C) There are inflection points at 
D) There is one inflection point at 
E) There are inflection points at , ,

Quizplus · Accepted Answer

In order to find the inflection point(s), we need to look for the point(s) where the second derivative changes sign. 
The first derivative of the given function is: 
f'(t) = 11ea8970_6a2f_03f4_861b_7572565f5620_TB1301_11'
= 11ea8970_6a2f_2b0c_861b_54b4ca4ec8cb_TB1301_11
Taking the derivative again, we get: 
f''(t) = 11ea8970_6a2f_2b0d_861b_25dcdfd9c86e_TB1301_11
Since the second derivative is a constant, it never changes sign. Therefore, there are no inflection points. The best choice is (A).

The Number of People Who Donated to a Certain Organization