Question

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

The exponential function in the table represents the student population of the county that Greeville is in, in years since 2010.
Years since 2010 2 3 4 5
Population 2200 4400 8800 17,600
How does the y-intercept of the exponential function compare to the y-intercept of the linear function? Drag the correct answer to the box to complete the statement.
approximately 300 more than
approximately 300 less than
approximately 2000 more than
approximately 2000 less than
The y-intercept of the exponential function is _______ the y-intercept of the linear function.

Answer 1

Answer: The y-intercept of the exponential function is approximately 2000 less than the y-intercept of the linear function.

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=
`(y_3)/(y_2)=(4400)/(2200)=2`

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

`2200=A(2)^2\\\Rightarrow\ A=(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.