Complete Question
The complete question is shown on the first uploaded image
Answer:
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
[tex]\frac{9300-9200}{5} = \frac{100}{5} =20[/tex]
So this means that after 9300 the next line segment is 9320
Considering the x-axis each line segment is
[tex]\frac{4-2}{4} = \frac{2}{4} = 0.5[/tex]
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
[tex](t_1,p_2) = (4.8, 9284) \ (t_2,p_2) = (5, 9320)[/tex]
The rate change
[tex]= \frac{p_2-p_1}{t_2-t_1}=\frac{9320-9284}{5-4.8} = \frac{36}{0.2} = 180[/tex]
So the rate is 180 thousand employer per year
C)
So to obtain the percentage rate of change of the function
Now
[tex]f(4.8) = 9284 \ Thousand[/tex]
[tex]f'(4.8) = 180 \ Thousand[/tex]
Note: This is so because differentiation is the same as slope of the graph
Hence the percentage rate of change
[tex]\frac{f'(4.8)}{f(4.8)} *\frac{100}{1} = \frac{180 \ 000}{9284 \ 000} * \frac{100}{1}[/tex]
= 1.939%
