The function f(x)=125(0.9)x models the population of a species of fly in millions after x years.How does the average rate of change between years 11 and 15 compare to the average rate of change between years 1 and 5?A) The average rate of change between years 11 and 15 is about 1/3 the rate between years 1 and 5.B) The average rate of change between years 11 and 15 is about 1/2 the rate between years 1 and 5 .C) The average rate of change between years 11 and 15 is about 3 times the rate between years 1 and 5.D) The average rate of change between years 11 and 15 is about 2 times the rate between years 1 and 5 .
Accepted Solution
A:
A word to the wise: It's f(x)=125(0.9)^x, where ^ represents exponentiation.
In this case the ave. value over the interval [11, 15] is
125(0.9)^15 - 125(0.9)^11 ------------------------------------- = (125/4) [ 0.9^15 - 0.9^11) 15 - 11 = (31.25) [ 0.2059 - 0.3138 ] = a negative result = (31.25)(-0.1079) = -3.372 (av. r. of c. over the interval [11,15] )
Do the same thing for the time interval [1,5]. Then compare the two rates of change.