Question

the number of banks in the country for selected years from 1980 to 2009 is given by y = -384.3x + 18023, where x is the number of years after 1980. if this model is accurate after 2009, in what year would the number of banks be 6,110? (do not round until the final answer, then round to the nearest whole number.) 2009 2011 2020 2013 question 37 (3 points) find the slope of the line that goes through the given points. (-9, 8), (6, -6) -2/3 -14/15 -15/14 14/15

Explanation:

First Sub - Question (Number of Banks)

Step 1: Set up the equation

We know the equation for the number of banks is \(y=- 384.3x + 18023\), and we want to find \(x\) when \(y = 6110\). So we set up the equation \(6110=-384.3x + 18023\).

Step 2: Solve for \(x\)

First, subtract 18023 from both sides: \(6110-18023=-384.3x\).
\(6110 - 18023=-11913\), so \(-11913=-384.3x\).
Then, divide both sides by \(- 384.3\): \(x=\frac{-11913}{-384.3}\).
\(x = 31\) (after calculation).

Step 3: Find the year

Since \(x\) is the number of years after 1980, the year is \(1980 + 31=2011\).

Step 1: Recall the slope formula

The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step 2: Identify the points

Here, \((x_1,y_1)=(-9,8)\) and \((x_2,y_2)=(6, - 6)\).

Step 3: Calculate the slope

Substitute the values into the formula: \(m=\frac{-6 - 8}{6-(-9)}=\frac{-14}{6 + 9}=\frac{-14}{15}\).

Answer:

2011

Second Sub - Question (Slope of the Line)