Question

Please help! The last tutors answer was wrong. They want the equation y = and answer for x.

Answer 1

Given that the graph of the Quadratic Equation must pass through these points:

`(0,25),(50,200),(100,275)`

• You know that the equation has this form:

`y=ax^2+bx+c`

Where:

`a\\e0`

You can use a calculator to find the corresponding Quadratic Equation that models the given situation:

1. Press the button MODE on your calculator.

2. Choose the option STAT for statistical calculations.

3. Choose the option for Quadratic Regression and enter the coordinates in the table.

4. Press the buttons SHIFT and STAT.

5. Calculate the regression.

You get that:

`\begin{gathered} a=-0.02 \\ b=4.5 \\ c=25 \end{gathered}`

Hence, the Quadratic Equation that models the data is:

`y=-0.02x^2+4.5x+25`

• In order to estimate the population in 2050, you need to substitute this value into the equation:

`x=150`

And evaluate:

`\begin{gathered} y=-0.02(150)^2+4.5(150)+25 \\ y=250 \end{gathered}`

Hence, the answer is:

- Equation:

`y=-0.02x^2+4.5x+25`

- Population in 2050:

`250\text{ }million\text{ }(approximately)`