Question

Robert manages a large farm and keeps his goats in two fenced areas. The number of goats in each of the two fenced areas can be modeled by the following functions, where t represents the number of months since Robert started managing the farm.

Answer 1

The functions are:

i) $f(t)=0.3t+12$

ii) $g(t)=0.1t^2-1.7t+15$, where f and g is the number (approximate) of goats in fence area 1, and fence area 2.


After t months, the total number of goats is:

$f(t)+g(t)=0.3t+12+0.1t^2-1.7t+15$, which adding the like terms simplifies to 

$f(t)+g(t)=0.1t^2-1.4t+27$.



Thus, our function is $h(t)=(t)+g(t)=0.1t^2-1.4t+27$.


Answer: $h(t)=0.1t^2-1.4t+27$.