Question

The linear function in the graph shows the population of Greeville in the years since 2010.

Answer 1

approximately 2000 less than is your answer.

Answer 2

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 :-

$y=Ab^x$, where A is the initial population and x is the number of years.

From table , the multiplicative rate of change b=$\frac{y_3}{y_2}=\frac{4400}{2200}=2$

Put x=2 and b=2 in the equation, we get

$2200=A(2)^2\\\Rightarrow\ A=\frac{2200}{4}=1950$

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 = $2500-550=1950\approx2000....\text{{Rounded nearest thousand}}$

Hence, The y-intercept of the exponential function is approximately 2000 less than the y-intercept of the linear function.