Assuming a linear relationship, find the linear equation that models the bee population based on the number of years after 2015.

Question

A beekeeper has been noticing a decline in the number of bees in his beehives. In 2015, he had 1,200 bees but by 2019 he had only 600 bees. Assuming a linear relationship, find the linear equation that models the bee population based on the number of years after 2015. At what point is it predicted that the bee population will be 0?

Answer 1

2019 had 600 bees, call that year 4 and count by 100's of bees, as "6" bees

2015 had 1,200 bees, call that year 0 with "12" bees

plot those two points (6, 4) and (12,0)

it has slope = 4/(6-12) = -4/6 = -2/3

the equation of the line is

y = -(2/3)x + b

plug in either point to find b

4= -(2/3)(6 + b

b = 4 +4 = 8

y intercept = b = 8 = the point (0,8)

y = -(2/3)x + 8

in year 8, the population = 0

year 8 is 2015+8 = 2023

the bees lose 150 bees per year

in 8 years they lose 8(150) = 1200 bees since 2015 when they had 1200 bees

This year is the year for zero bee population: 2023