The length C (t), in inches, of a channel catfish in an Iowa river t years after the first year of life can be approximated by the linear function C. Some values of C (t) are given in the table above.
F (t) = 3t + 4
The length F (t), in inches, of a flathead catfish in the same Iowa river t years after the first year of life can be approximated by the linear function F, defined by the equation above.
According to the model, which of the following is the closest to the expected age, to the nearest whole year, of a flathead catfish that is 31 inches long?

The correct answer is: 10 years old

Hint:
Length of the flatheaded catfish = F (t) = 31 inches.
To find - age of this catfish
Step-by-step solution:-
F (t) = 3t + 4
∴ 31 = 3t + 4
∴ 31 - 4 = 3t
∴ 27 = 3t
∴ = t -----------------------  (Dividing both sides by 3)
∴ 9 = t
Since t is the age of a fish after first year of life,
Closest expected age of the fish = t + 1 = 9 + 1 = 10
Final Answer:
Option A i.e. 10 years old is the correct Option.
Note:
Alternatively, we can substitute the ages (age-1) given in each option and check whether the answer comes to 34 inches-
A. 10 years old. Since t = age after 1^st year, t = 10 - 1 = 9
F (t) = 3t + 4
F (9) = 3 (9) + 4
F (9) = 27 + 4
F (9) = 31 inches
B. 13 years old. Since t = age after 1^st year, t = 13 - 1 = 12
F (t) = 3t + 4
F (12) = 3 (12) + 4
F (12) = 36 + 4
F (12) = 40 ≠ 31
C. 98 years old. Since t = age after 1^st year, t = 98 - 1 = 97
F (t) = 3t + 4
F (97) = 3 (97) + 4
F (97) = 291 + 4
F (97) = 295 ≠ 31
D. 106 years old. Since t = age after 1^st year, t = 106 - 1 = 105
F (t) = 3t + 4
F (105) = 3 (105) + 4
F (105) = 315 + 4
F (105) = 319 ≠ 31