If the average rate of change of g(x) from x = 7 to x = 10 is -80, and if g(7) = 400, then find g(10).
g(10)=460
using y=mx+b
m= -80
substitute the info given, g(7)=400
400 = -80(7) + b
b=960
substitute m & b into the equation;
g(x)= -80x + 960
substitute g(10) into the new equation
g(10)= -80(10)+960
g(10)= 160
SORRY, ABOUT THE LAST POST :)
So you have 2 points, (7,400) and (10-7) = -80
,y) where the slope = -80
(y-400)/(10-7) = -80
y-400 = -240
y = 160 , or g(10) = -240
To find g(10), we need to use the average rate of change and the value of g(7). The average rate of change of a function from x = a to x = b is given by the formula:
average rate of change = (g(b) - g(a)) / (b - a)
In this case, a = 7, b = 10, and the average rate of change is given as -80. We are also given the value of g(7) as 400.
Using the formula for average rate of change, we can write:
-80 = (g(10) - 400) / (10 - 7)
Simplifying the equation:
-80 = (g(10) - 400) / 3
Multiply both sides of the equation by 3:
-240 = g(10) - 400
Now, isolate g(10) by adding 400 to both sides:
g(10) = -240 + 400
g(10) = 160
Therefore, g(10) is equal to 160.