Question

The equation, y = 1250x + 22,850, gives the salary of a person as "y" after the stated number of years (x). Model the data with a linear function using the points (1, 24,100) and (3, 36,600) Then use this function to predict the salary in 5 years.

Answer 1

Answer:

(a) $y = 6250x +17850$ --- The function

(b) $y = 49100$ --- The salary in 5 years

Step-by-step explanation:

Given

$y = 1250x + 22850$

Solving (a): Model the function around (1,24100) and (3,36600)

First, we calculate the slope

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{36600 - 24100}{3 - 1}$

$m = \frac{12500}{2}$

$m = 6250$

The function is then calculated as:

$y = m(x - x_1) + y_1$

$y = 6250(x - 1) + 24100$

$y = 6250x - 6250 + 24100$

$y = 6250x +17850$

Solving (b): Salary in 5 years

Here:

$x = 5$

So:

$y = 6250x +17850$

$y = 6250*5 +17850$

$y = 49100$