Please help, I am so confused

Question

The population of Anytown, USA decreased from 2,435 in 1995 to 1,650 in 2005. Find the average rate of change in the population over the ten-year period, and provide the linear equation that represents the population decrease.

Answer 1

(2.435, 0) and (1.650, 10) = (x,y) are points on a line where x = thousands, and y = number of years after 2000

slope of the line = 10/(2.435-1.65) = -10/.785 =about -12.74

y= -12.74x + b solve for b by plugging in either point

0 = -12.74(2.435) + b

b = 31.022

y = -12.74x + 31.02 is a linear equation where y = the year and x = the population in thousands

in about the year 2031, every has died off or moved, so the population = zero

anytown USA is a dying city, in more ways than one.

BUT you probably want to reverse x and y to get

-12.74x = y-31.02

x = -y/12.74 + 31.02/12.74

x = -.0785y + 2.435 where when y=0 representing the year 2000, population is 2.435 thousand

average annual rate of change = negative 7.85%, = the coefficient of y, = slope = derivative = x'(y)