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
Mademuasel [1]
3 years ago
9

The Pacific halibut fishery has been modeled by the differential equation dy dt = ky 1 − y K where y(t) is the biomass (the tota

l mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be K = 6×107 kg, and k = 0.78 per year. (a) If y(0) = 2×107 kg, find the biomass a year later. (Round your answer to two decimal places.) .52 Incorrect: Your answer is incorrect. ×107 kg (b) How long will it take for the biomass to reach 4×107? (Round your answer to two decimal places.) years
Mathematics
1 answer:
Dafna1 [17]3 years ago
8 0

Answer:

a. The biomass weighs 2.30 * 10^7 kg after a year

b. It'll take 2.56 years to get to 4*10^7kg

Step-by-step explanation:

a.

k = 0.78,K = 6E7 kg

Given

dy/dt = ky(1- y/K)

Make ky dt the subject of formula

ky dt = dy/(1-y/K) --- make k dt the subject of formula

k dt = dy/(y(1-y/K))

k dt = K dy / y(K-y)

k dt = ((1/y) + (1/(K-y)))dy ---- integrate both sides

kt + c = ln(y/(K-y))

Ce^(kt) = y/(K-y)

Substitute the values of k and K

Ce^(0.78t) = y/(6*10^7 - y) ----- (1)

Given that y(0) = 2 * 10^7kg

(1) becomes

Ce^(0.78*0) = (2 * 10^7)/(6*10^7 - 2*10^7)

Ce° = (2*10^7)/(4*10^7

C = 2/7

Substitute 2/7 for C in (1)

2/7e^0.78t = y/(6*10^7 - y) ---(2)

We're to find the biomass a year later

So, t = 1

2/7e^0.78 = y/(6*10^7 - y)

0.62 = y/(6*10^7 - y)

y = 0.62(6*10^7 - y)

y = 0.62*6*10^7 - 0.62y

y + 0.62y = 0.62*6*10^7

1.62y = 0.62*6*10^7

1.62y = 3.72 * 10^7

y = 2.30 * 10^7kg.

Hence, the biomass weighs 2.30 * 10^7 kg after a year

b.

Here, we're to calculate the time it'll take the biomass to get to 4*10^7 kg

Substitute 4*10^7 for y in (2)

2/7e^0.78t = 4*10^7/(6*10^7 - 4*10^7)

2/7e^0.78t = 4*10^7/2*10^7

2/7e^0.78t = 2

e^0.78t = (2*7)/2

e^0.78t = 2

t = 2 * 1/0.78

t = 2.56 years

Hence, it'll take 2.56 years to get to 4*10^7kg

You might be interested in
Please help me lol a lil confused
alex41 [277]

\leadsto f( \rm x) =  - (x - 3)(x - 5)

\\  \\

\leadsto f( \rm x) =   - ( {x}^{2}  - 5x - 3x + 15) \\

\\  \\

\leadsto f( \rm x) =   - ( {x}^{2}   - 8x + 15) \\

\\  \\

\leadsto f( \rm x) =   - {x}^{2}  + 8x  -  15 \\

3 0
2 years ago
Read 2 more answers
The graph shows the distance traveled by two runners over several minutes,
ElenaW [278]

Runner B is going slower.

7 0
3 years ago
Read 2 more answers
99 POINTS PLZ HELP Which explanation best describes the answer to this problem? At the honey farm there were 35 bees in a hive.
LiRa [457]

Answer:

910 bees

Step-by-step explanation:

There are 35 bees in a hive and we have 26 hives.

Take the number of hives and multiply by the number of bees per hive

26*35 =910

There are 910 bees total

7 0
3 years ago
Read 2 more answers
Can someone make 3 or more equations with 2 variables on both sides, in a fraction, integer, and decimal form?
Goryan [66]

hi it could be 3x+2=180 , 3/4x+19=189, 3.4x+12=100

8 0
3 years ago
Solve y=(x-1)^ +4
Dimas [21]

Answer:

,nm

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • How to order the following fractions<br><br> 3/4 9/16 3/16 7/8 3/8
    13·2 answers
  • What is the measurement of
    13·2 answers
  • What is the smallest subset that 46 belongs to
    8·1 answer
  • Help me please i wish i can get somehelp
    10·1 answer
  • The graphs of g(x) = x³- ax² + 6 and h(x) = 2x² + bx + 3 touch when x = 1. Therefore, the tangent to
    9·1 answer
  • Advantage of quality control to the producer and to the customer​
    12·1 answer
  • Find the quotient: 6/2 divided by 3/4.
    10·2 answers
  • Will mark brainiest!!!
    7·1 answer
  • Answer please i will give brainliest
    5·1 answer
  • What are the factors of 2x2 3x – 54? Select two options. 2x – 9 2x – 6 2x 6 x – 6 x 6.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!