Question

In 1933, Riatt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula

L = 53 − 42.82 × 0.82t.
(a) Calculate L(5). (Round your answer to two decimal place.)
cm
Explain what it means.
It means a haddock that is 5 years old is approximately that length.It is approximately 1/5 of the haddock's length when the haddock is 5 years old. It is the haddock's age at 5 centimeters.It means a haddock that is 5 years old will grow to exactly that length.

Answer 1

To calculate the length of a haddock at 5 years old using the given formula, we substitute 5 for t and find that L(5) is approximately 41.77 cm. This measurement signifies the estimated length of a haddock at that age.

Step-by-step explanation:

To calculate L(5) using the given formula L = 53 - 42.82 × 0.82t, where L is the length of haddock in centimeters and t is the age in years, we substitute t with 5:

L(5) = 53 - 42.82 × 0.825

Using a calculator, we find:

L(5) = 53 - 42.82 × (0.82 × 0.82 × 0.82 × 0.82 × 0.82)

L(5) = 53 - 42.82 × 0.262144

L(5) = 53 - 11.23112688

L(5) = 41.76887312 ≈ 41.77 cm

So, a haddock that is 5 years old is approximately 41.77 cm long. This answer provides us a way to estimate the length a haddock will attain at a certain age, which is important for fisheries and marine biologists studying the growth patterns of fish.

Answer 2

a) If the length of haddock in centimeters in 1993 is given as L = 53 − 42.82 × 0.82t, using a linear equation, five yeas after, the length L(5) of the haddock is 6.08 centimeters.

b) The above-calculated length of a haddock means D) It means a haddock that is 5 years old will grow to exactly that length.

A linear equation of the slope-intercept form is written as y = mx + b, where m is slope, b is the y-intercept, and x refers to the period interval.

The given formula for the length of haddock in centimeters in 1993 is:

L = 53 − 42.82 × 0.82t

a) L(5) = 53 − 42.82 × 0.82(5)

= 53 - 42.82 x 4.1

= 6.08 centimeters

Thus, we can conclude that at 5, the length of the haddock is exactly 6.08 centimers.

Complete Question:

In 1933, Riatt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula

L(t) = 53 − 42.82 × 0.82t.

(a) Calculate L(5). (Round your answer to two decimal place.)

Explain what it means.

A) It means a haddock that is 5 years old is approximately that length.

B) It is approximately 1/5 of the haddock's length when the haddock is 5 years old.

C) It is the haddock's age at 5 centimeters.

D) It means a haddock that is 5 years old will grow to exactly that length.