The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)

Table below represents the displacement of a fish from its reef as a function of time:

Time

(hours)

(x)       Displacement  from reef

(feet)  (y)

0                        4

1                       64

2                      124

3                      184

4                      244

Part A

To find the y-intercept, put x=0 and find for y;

As you can see from the the table when x=0 , y=4 this means, that the fish started off 4 feet away from its reef

At 0 hours, the distance its away from its reef is, 4 feet

Part B

The average rate of change of the function calculates the slope of the line or a curve on a given range.

For any point the slope between the ordered pairs (1, 64) and (3, 184).

the formula of slope is given by:

Slope

The average rate of the change of function represented by the table between x=1 to x=3 hours is, 60.

The average rate represents the speed of the fish in feet\ hour.

Part C:

To find the domain of the function :

Now, we know the slope and the y-intercept we can easily find the equation of the line where m is the slope and b is the y-intercept.

∵ m =60 and b=4, we have ,

if the fish continued to swim at this rate until it traveled 724 feet from the reef.

⇒

On simplify we get;

∴the fish would take 12 hours to traveled 724 feet from the reef.

so, the domain of the function would be between 0 and 12.

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.