The length (in centimeters) of a typical Pacific halibut t years old is approximately . What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?
A) 151.2 cm; 0.957 cm/yr; 226 cm;
B) 138.1 cm; 11.6 cm/yr; 199 cm;
C) 199.0 cm; 13.7 cm/yr; 253 cm;
D) 108.3 cm; 12.3 cm/yr; 199 cm;

Question

The length (in centimeters) of a typical Pacific halibut t years old is approximately  . What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?
A) 151.2 cm; 0.957 cm/yr; 226 cm; 
B) 138.1 cm; 11.6 cm/yr; 199 cm; 
C) 199.0 cm; 13.7 cm/yr; 253 cm; 
D) 108.3 cm; 12.3 cm/yr; 199 cm;

Quizplus · Accepted Answer

- To find the length of a typical 6-year-old Pacific halibut, substitute t=6 into the given function: 11eaa8b1_dada_c73e_b1b6_454bcc3be3cf_TB6026_11 = 59.1 + (11.6 * log(6)). This results in approximately 138.1 cm.
- To find the rate of increase of the length of a typical 6-year-old Pacific halibut, take the derivative of the given function with respect to t and evaluate it at t=6: (11.6 / (t * ln(10))). Substituting t=6 into this expression gives approximately 11.6 / (6 * ln(10)) = 0.957 cm/yr.
- To find the maximum length a typical Pacific halibut can attain, set the derivative of the given function with respect to t equal to zero and solve for t. This gives t = e^(4.877) (which is approximately 130.5 years). Substituting this value of t into the given function gives the maximum length as approximately 199 cm.

The Length (In Centimeters) of a Typical Pacific Halibut T