Answer:
t=2
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
We have points (3,10) and (5,t) and the slope is -4
Substituting these in
-4 = (t-10)/ (5-3)
Simplifying
-4 = (t-10) / 2
Multiply by 2 on both sides
-4 = (t-10) / 2 *2
-8 = t-10
Add 10 on both sides
-8+10 = t-10+10
2 = t
Average rate of change can be calculated by determining the
rate of change at x = a, and at x = b
f’(x) =2 (3^x) ln(3)
f’(0) = 2 ln(3)
f’(1) = 6 ln(3)
f’(2) = 18 ln(3)
f’(3) = 54 ln(3)
Average:
at section A = [6 ln(3) – 2 ln(3)]/1 = 4 ln(3)
at section B = [54 ln(3) – 18 ln(3)]/1 = 36 ln(3)
section B is 9 times larger.
Based from the f’(x), f’(x) varies as the power of x. so the
greater of value of x, the greater the rate of change.
