Answer: The y-intercept of the exponential function is approximately 2000 less than the y-intercept of the linear function.
Step-by-step explanation:
Given: The exponential function in the table represents the student population of the county that Greenville is in, in years since 2010.
The standard exponential function is given by :-
[tex]y=Ab^x[/tex], where A is the initial population and x is the number of years.
From table , the multiplicative rate of change b=[tex]\frac{y_3}{y_2}=\frac{4400}{2200}=2[/tex]
Put x=2 and b=2 in the equation, we get
[tex]2200=A(2)^2\\\Rightarrow\ A=\frac{2200}{4}=1950[/tex]
We know that the value of y intercept occurs when x=0,
From the given table , the y intercept of exponential function (Initial population)= 550
The linear function in the graph shows the population of Greenville in the years since 2010.
From the given graph, the y intercept of linear function (x=0 for year 2010)= 2500
The difference in y intercepts = [tex]2500-550=1950\approx2000....\text{{Rounded nearest thousand}}[/tex]
Hence, The y-intercept of the exponential function is approximately 2000 less than the y-intercept of the linear function.
