(a) Estimate a second point on the tangent line. (t, p) = Correct: Your answer is correct. (b) Calculate the rate of change of the function at the labeled point. (Round your answer to one decimal place.) 12.5 Incorrect: Your answer is incorrect. thousand employees per year (c) Calculate the percentage rate of change of the function at the labeled point. (Round your answer to three decimal places.) 0.833 Incorrect: Your answer is incorrect. % per year

Complete Question

The complete question is shown on the first uploaded image

a

The Estimated  second point is (t,p) =(5,9320)

b

The rate is 180 thousand employer per year

c

The percentage rate of change of the function is 1.939%

Step-by-step explanation:

Looking at the graph

  First is to obtain the scale of the graph what i mean is what the distance between each line segment

    Considering the y-axis  each line segment is

So this means that after 9300 the next line segment is 9320

Considering the x-axis each line segment is

What this means is that 2 line segment after 4 is 4 +2 ×(0.5) =5

So looking this two points (new_t,new_p) = (5 , 9320) = we see that they form a coordinate

       B) The labeled point that we are to consider are

The rate change

So the rate is 180 thousand employer per year

C)

 So to obtain the percentage rate of change of the function

   Now

Note: This is so because differentiation is the same as  slope of the graph

    Hence the percentage  rate of change

                           = 1.939%

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction