The number of female nurses in a country can be predicted using the function f(t)=7,300 + 25t, where t is the number of years since 2000. The number of male nurses can be predicted using the function m(t) = 2,500(1.02)t, where t is the number of years since 2000. About how many years will it take before the number of male nurses is expected to exceed the number of female nurses?

2.9 years

Step-by-step explanation:

Female nurses function f(t)= 7300 + 25t

Male nurses function m(t) = 2500 (1.02)t = 2550t

In order to make the male nurses exceed female nurses we need to create the inequality like

Male nurses female nurses

2550t     7300 + 25t

2525t     7300

t  

t  2.891 ≈ 2.9 years

So in 2.9 years the No of Male nurses will exceed female nurses

Let check our answer

Female nurse after 2.9 years = 7300 + 25*2.9 = 7372.5

Male nurses after 2.9 years = 2550.2.9 = 7395

Clearly male nurses are more that female nurses after 2.9 years