Identify the sequence graphed below and the average rate of change from n = 0 to n = 2.coordinate plane showing the point 1, 10, point 2, 5, and point 4, 1.25(5 points) an = 10( one half )n − 1; average rate of change is fifteen halves an = 10( one half )n − 1; average rate of change is negative fifteen halves an = 20( one half )n − 1; average rate of change is fifteen halves an = 20( one half )n − 1; average rate of change is negative fifteen halves
Accepted Solution
A:
The answer would be: an = 10( one half )n − 1; average rate of change is negative fifteen halves.
This question is about exponent function/series. You are given 3 points from the function, point A (1,10), point B( 2, 5) and point C(4,1.25). If you insert point A to the function, an = 10( one half )^n − 1 will give a result of 10 for n=1.
For n=0, the result would be: an = 10( one half )^n − 1 an= 10(1/2)^0-1 an= 10(1/2)^-1= 10* 2= 20
Then the average rate of change from n=0 to n=2 would be: Rate of change= (y2-y1)/ (x2-x1) Rate of change= (5-20)/ (2-0)= -15/2= negative fifteen halves