1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
slava [35]
3 years ago
10

The length of some fish are modeled by a von Bertalanffy growth function. For Pacific halibut, this function has the form L(t) =

200(1 – 0.956e–0.18t ) where L(t) is the length (in centimeters) of a fish t years old.
(a) Find the rate of change of the length as a function of time
(b) In this part, give you answer to the nearest unit. At what rate is the fish growing at age:______.
t= 0 cm/yr
t= 1 cm/yr
t= 6 cm/yr
(c) When will the fish be growing at a rate of 6 cm/yr? (nearest unit)
Mathematics
1 answer:
Dafna1 [17]3 years ago
7 0

Answer:

a) L'(t) = 34.416*e^(-0.18*t)

b) L'(0) = 34 cm/yr , L'(1) =29 cm/yr , L'(6) =12 cm/yr

c) t = 10 year                                          

Step-by-step explanation:

Given:

- The length of fish grows with time. It is modeled by the relation:

                                   L(t) = 200*(1-0.956*e^(-0.18*t))

Where,

L: Is length in centimeter of a fist

t: Is the age of the fish in years.

Find:

(a) Find the rate of change of the length as a function of time

(b) In this part, give you answer to the nearest unit. At what rate is the fish growing at age: t = 0 , t = 1, t = 6

c) When will the fish be growing at a rate of 6 cm/yr? (nearest unit)

Solution:

- The rate of change of length of a fish as it ages each year  can be evaluated by taking a derivative of the Length L(t) function with respect to x. As follows:

                             dL(t)/dt = d(200*(1-0.956*e^(-0.18*t))) / dt

                             dL(t)/dt = 34.416*e^(-0.18*t)

- Then use the above relation to compute:

                            L'(t) = 34.416*e^(-0.18*t)

                            L'(0) = 34.416*e^(-0.18*0) = 34 cm/yr

                            L'(1) = 34.416*e^(-0.18*1) = 29 cm/yr

                            L'(6) = 34.416*e^(-0.18*6) = 12 cm/yr

- Next, again use the derived L'(t) to determine the year when fish is growing at a rate of 6 cm/yr:

                             6 cm/yr = 34.416*e^(-0.18*t)

                             e^(0.18*t) = 34.416 / 6

                             0.18*t = Ln(34.416/6)

                             t = Ln(34.416/6) / 0.18

                             t = 10 year

You might be interested in
What is 5/9 as a decimal and percent?
ale4655 [162]
The answer is 0.555556 I really hope this helps!                      
3 0
3 years ago
Read 2 more answers
Why do we need to lean stuff that we dont need in the real world???
DanielleElmas [232]

Answer:

Teachers are idiots that's why :)

6 0
3 years ago
Read 2 more answers
two planes traveling in opposite directions leave the airport at the same time. in 4 hours they are they are 2900 miles apart. i
marta [7]
I Got 650 miles per hour
6 0
3 years ago
Help please rn please help
Anvisha [2.4K]

Answer: the answer is MO=5

Step-by-step explanation:

6 0
1 year ago
PLEASE PLEASE PLEASE HELP!! Explanations on how to set it up would be great!
faltersainse [42]
Opposite sides of a parallelogram are congruent.
3x+ 2= 4x-3
Subtract 3x from both sides
2= x -3
Add 3 to both sides
5= x

2y+7=4y-9
Subtract 2y from both sides
7= 2y -9
Add 9 to both sides
16 = 2y
Divide by 2 on both sides
8 = y
8 0
3 years ago
Other questions:
  • Darius is studying the relationship between mathematics and art. He asks friends to each draw a "typical” rectangle. He measures
    11·2 answers
  • If john ran 5 kilometer marathon ,how long was that in meters
    7·2 answers
  • What are some items that are less than 1 ounce<br> What are some items that weigh more than 1 ton
    7·1 answer
  • At a local high school, 30% of the students are on a school sports team, 25% take at least one Advanced Placement (AP) class, an
    5·1 answer
  • You randomly guess the answers to two questions on a multiple-choice test. Each question has three choices: A, B, and C.
    7·1 answer
  • I need help with area of a rectangle! Plese help me out this is a starr review!
    12·1 answer
  • 1. a.) Find the Surface Area and Volume of the right prism. Surface Area: 9 am Volume: LE 6 cm 17 cm​
    13·1 answer
  • Solve the equation for y y−5x=3
    8·1 answer
  • . Two stacks of flashcards each contain a card with one of the digits 0-9 written on the card. What is the probability of drawin
    12·1 answer
  • Please see attached photo for question
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!