Question

The Michigan veteran population in 1990 was 14.2% and in 2000 was 12.4%.

a) Let P represent the percent of Michiganders who were veterans and t represent the years since 1990. Find a linear model of this situation, rounding to two decimal places.

P(t)=

Answer 1

Let x- intercept represents time

Let y-intercept represents population

Let 1990 represent initial year

Points are (0,14.2)(10,12.4)

slope m=
`(y2-y1)/(x2-x1)`

=
`(12.4-14.2)/(10-0) =(-1.8)/(10) = -0.08`

General linear equation

y= mx+b --------------(i)

here m is slope and b is intercept

plug the 1st point in equation

14.2= -0.018(0) + b

b=14.2

y= 0.018x + 14.2

replace y with p(t) and x with t

p(t) = -0.018t + 14.2