Problema Solution
A company has determined that the mouse population in their basement can be modeled by a linear function depending on the year. When they moved into their building in 1989, the mouse population was 320 mice. In 2002, the discovered that the mouse population has increased to 503 mice. If this growth is to continue linearly, then how many mice are in the basement in 2014? Set up and solve an appropriate linear function.
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let
y = the number of mice
x = the number of years passed since 1989
y = ax + b, where a and b are constants
for x = 0 years we have y = 320 mice or:
320 = a*0 + b
b = 320
for x = 2002 - 1989 = 13 years we have y = 503 mice or:
a*13 + 320 = 503
by solving we find:
a = 183/13
click here to see the step by step solution of the equation:
the linear function is:
y = (183/13)x + 320
for the year of 2014 we have:
x = 2014 - 1989
x = 25 years
y = (183/13)*25 + 320
y = 672 mice approximately
there are 672 mice in the basement in 2014.