Question

Drag each ote to the correct box. Not all tiles will be used The table represents the balance of Sylvia's loan, y over a period of 24 months. She used technology to create the scatter plot shown and determined the best fit equation to model the data y=-382.05x=25,07740. Determine how long it will take to reach the green balances.the balance of the loan will be approximately $17,000.__________the balance of the loan will reach $0_________

Answer 1

The given model is as given below

$y=-382.05x+25077.4$

Find the value of x when y= $17000 as shown below

$\begin{gathered} 17000=-382.05x+25077.4 \\ 17000-25077.4=-382.05x \\ -8077.4=-382.05x \\ x=\frac{-8077.4}{-382.05} \\ x=21.14 \end{gathered}$$x\approx21months$

The value of x when y = $0 is as shown below

$\begin{gathered} 0=-382.05x+25077.4 \\ -382.05x=-25077.4 \\ x=\frac{-25077.4}{-382.05} \\ x=65.639\text{months} \\ x\approx66months \end{gathered}$

Hence, when the loan balance is $17,000, it will take 21 months. While, when the loan is $0, it will take 66 months