20. The model for the frog population was given by the function F(m)=m+6, and the model for the turtle population was given by the function T(m)=m^2+3/m+1. Which of the following expressions defines the function F(m)-T(m), the difference in size between the two populations m months after the initial count?
Answer: C
F(m) - T(m) is defined by the expression 7m + 3/(m + 1).
To find the difference in size between the frog population and the turtle population, we calculate F(m) - T(m). The resulting expression simplifies to 7m + 3/(m + 1), which matches option C.
A) 7m + 9/(m + 1)
This option is incorrect because it suggests a different constant term in the numerator. The difference in size must reflect the correct simplification of F(m) - T(m), which does not yield 9 in the numerator.
B) -7m - 3/(m + 1)
This option is also incorrect as it indicates a negative difference. The correct calculation shows that the frog population is larger than the turtle population, leading to a positive difference.
C) 7m + 3/(m + 1)
This option is correct because it accurately represents the simplified expression obtained from F(m) - T(m). When calculated, this expression reflects the difference in population sizes after m months.
D) #NAME?
This option is invalid as it does not provide a recognizable mathematical expression. It cannot be assessed as a possible answer to the question.
E) #NAME?
Similar to option D, this is also an invalid choice without any recognizable content, rendering it irrelevant for consideration.
Conclusion
The correct expression for the difference in size between the frog and turtle populations is 7m + 3/(m + 1), as indicated in option C. All other options either misrepresent the calculation or provide invalid expressions, confirming that C is the only correct choice based on the mathematical model provided.