The life expectancy E , in solar lifetimes, of certain stars depends on their mass M , in solar masses. The relationship is $E = M ^ { - 25 }$ As mass increases, life expectancy decreases. What can you say about the rate of decrease? A graph of E versus M can help you answer this question.
A) Life expectancy decreases at a decreasing rate.
B) Life expectancy decreases at an increasing rate.
C) Life expectancy reaches a point of inflection.
D) None of the above.

Question

The life expectancy E , in solar lifetimes, of certain stars depends on their mass M , in solar masses. The relationship is $E = M  ^ { - 25 }$ As mass increases, life expectancy decreases. What can you say about the rate of decrease? A graph of E versus M can help you answer this question.
A) Life expectancy decreases at a decreasing rate.
B) Life expectancy decreases at an increasing rate.
C) Life expectancy reaches a point of inflection.
D) None of the above.

Quizplus · Accepted Answer

The given relationship $E = M^{-2.5}$ indicates that as the mass $M$ increases, the life expectancy $E$ decreases, but the rate of decrease slows down because the exponent is negative. This means that for larger values of $M$, the decrease in $E$ for each unit increase in $M$ becomes smaller, indicating a decreasing rate of decrease.

The Life Expectancy E , in Solar Lifetimes, of Certain E=M−25E = M ^ { - 25 }E=M−25

The Life Expectancy E , in Solar Lifetimes, of Certain $E = M ^ { - 25 }$