The table below represents the distance of an airplane from its destination as a function of time: time (hours) x distance (miles) y 0 2,700 1 2,160 2 1,620 3 1,080 4 540 part a: what is the y-intercept of the function, and what does this tell you about the airplane? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the airplane continued to travel at this rate until it reached its destination? (2 points)

Part A) the Y intercept is where x = 0.

 Y intercept = 2,700. This means the plan is 2700 miles away from it's destination

Part B) at X1 y = 2160

X4 y = 540

rate of change = y2-y1 over x2-x1 using X4 and X1

rate of change = 540 -2160 / 4-1 = -1620/3 = -540

 for every 1 hour traveled the plane is  getting 540 miles closer to it's destination

Part C) the domain would be all the X numbers

 so at hour 4 it is 540, the rate of change is also 540 so at hour 5 it would be at it's destination so the domain would be (0,1,2,3,4,5)

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752