the complete question in the attached figure
we know that
When comparing raises, a fixed dollar increase can be modeled by a linear function and a fixed percent increase can be modeled by an exponential function
Part 1)
Let
t -------> represents the number of elapsed months
S(t)----> the functions that represent the monthly workforce
company A
Sa(t)=100+31*t
company B
Sa(t)=100*(1.10)^t
using a graph tool
see the attached figure N 2
the point of intersection both graphs are
(0,100) and (21,759)
t=21 months
S=759 employees
therefore
the answer part 1)
company B will have more employees than company A as of month 22
Part 2)
Let
t -------> represents the number of elapsed years
S(t)----> the functions that represent the yearly salaries
Employee A
Sa(t)=18+1.5*t
Employee B
Sa(t)=18*(1.04)^t
using a graph tool
see the attached figure N 3
the point of intersection both graphs are
(0,18) and (34.58,69.87)
therefore
the answer part 2)
employee B will earn more than employee A as of year 35
