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The population of fish, P, in a lake is a function of time, t, measured in years. The rate of cha...
A small lake is stocked with a certain species of fish. The fish population is modeled...
A small lake is stocked with a certain species of fish. The fish population is modeled by the function P = 12 1 + 4e−0.4t where P is the number of fish in thousands and t is measured in years since the lake was stocked. (a) Find the fish population after 4 years. (Round your answer to the nearest whole fish.) fish (b) After how many years will the fish population reach 6000 fish? (Round your answer to two decimal...
A species of fish was added to a lake. The population size P(t) of this species...
A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. P(t)= 1200 -0.42t 1+ 3e Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary. Initial population size: fish Population size after 9 years: fish...
2. Let L(t) = the length (in cm) of a fish at time t (in years). Suppose that the fish grows at a dL dt = 5.0e-0.2t rate (a) Determine the exact change in length of the fish between times t 5 and t 1...
2. Let L(t) = the length (in cm) of a fish at time t (in years). Suppose that the fish grows at a dL dt = 5.0e-0.2t rate (a) Determine the exact change in length of the fish between times t 5 and t 10. (Suggestion: First solve the differential equation using anti-differentiation.) Does the answer to this question depend on the initial condition L(0)? (b) Determine L(t) if L(0)=2 2. Continued (c) Find the approximate change in length of...
In t years, the population of a certain city grows from 500,000 to a size P...
In t years, the population of a certain city grows from 500,000 to a size P given by P(t) = 500,000 + 8000+?. dP a) Find the growth rate dt b) Find the population after 10 yr. c) Find the growth rate at t= 10. d) Explain the meaning of the answer to part (c).
If p is the price in dollars of computer mice at time, t, then we can think of price as a function of time. Similarly,...
If p is the price in dollars of computer mice at time, t, then we can think of price as a function of time. Similarly, 1. then number of computer mice demanded by consumers at any time, and the number of computer mice supplied by producers at any time, may also be considered as functions of time as well as functions of price. Both the quantity demanded and the quantity supplied depend not only on the price, but also on...
Problem #6: A model for a certain population P(1) is given by the initial value problem dP-H10-3-10-13 P), dt P(0)= 100000000, where t is measured in months (a) What is the limiting value of the popu...
Problem #6: A model for a certain population P(1) is given by the initial value problem dP-H10-3-10-13 P), dt P(0)= 100000000, where t is measured in months (a) What is the limiting value of the population'? (b) At what time (i.e., after how many months) will the populaton be equal to one half of the limiting value in (a)? Do not round any numbers for this part. You work should be all symbolic.) Problem #6(a): 10000000000 Enter your answer symbolically,...
3. A plant produces starch dependig on the intensity of heat it receives during the day. Assume the rate of starch production of the plant is 2 grams per hour dt +t where time t is measured in hours...
3. A plant produces starch dependig on the intensity of heat it receives during the day. Assume the rate of starch production of the plant is 2 grams per hour dt +t where time t is measured in hours and S(t) is the amou noon each day (time t = o is noon, t-1 is 1pm and so on). of starch produced t hours after a. Estimate the tot al change in S(t) between 1pm and 3pm using the right-hand...
The size of a certain insect population at time t (in days) obeys the function P(t)...
The size of a certain insect population at time t (in days) obeys the function P(t) = 400 0.00 (a) Determine the number of insects att=0 days. (b) What is the growth rate of the insect population? (c) What is the population after 10 days? (d) When will the insect population reach 560? (e) When will the insect population double? (a) What is the number of insects att=0 days? insects Enter your answer in the answer box and then click...
To protect the endangered species, some leatherback sea turtles are introduced into a protected ecosystem. The following function models the population of leatherback sea turtles, P as a function of the time, t in years, since they are introduced in the p
To protect the endangered species, some leatherback sea turtles are introduced into a protected ecosystem. The following function models the population of leatherback sea turtles, P as a function of the time, t in years, since they are introduced in the protected ecosystem P(t)=50+16t/2+0.1t https://i.gyazo.com/6e841f27ba9baa591cedde57db932a8f.png a. What is the initial number of leatherback sea turtles introduced into the protected ecosystem?b. Graph the population of leatherback sea turtles for the next 100 years.c. Determine is the range of the model.d. How many leatherback sea...
please answer 2d, 2e, and 2f and ahow all work. The graph below represents the growth of a certain population. The p...
please answer 2d, 2e, and 2f and ahow all work.
The graph below represents the growth of a certain population. The population is in thousands and the time is in years. Use it to answer the following questions 2. 4 time a. What is the initial population? Use function notation to express your answer. b. What is the average rate of change in the population from year 2 to year 3? Illustrate on the graph above the line that shows...
A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. P(t)= 1200 -0.42t 1+ 3e Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary. Initial population size: fish Population size after 9 years: fish...
2. Let L(t) = the length (in cm) of a fish at time t (in years). Suppose that the fish grows at a dL dt = 5.0e-0.2t rate (a) Determine the exact change in length of the fish between times t 5 and t 10. (Suggestion: First solve the differential equation using anti-differentiation.) Does the answer to this question depend on the initial condition L(0)? (b) Determine L(t) if L(0)=2 2. Continued (c) Find the approximate change in length of...
In t years, the population of a certain city grows from 500,000 to a size P given by P(t) = 500,000 + 8000+?. dP a) Find the growth rate dt b) Find the population after 10 yr. c) Find the growth rate at t= 10. d) Explain the meaning of the answer to part (c).
If p is the price in dollars of computer mice at time, t, then we can think of price as a function of time. Similarly, 1. then number of computer mice demanded by consumers at any time, and the number of computer mice supplied by producers at any time, may also be considered as functions of time as well as functions of price. Both the quantity demanded and the quantity supplied depend not only on the price, but also on...
Problem #6: A model for a certain population P(1) is given by the initial value problem dP-H10-3-10-13 P), dt P(0)= 100000000, where t is measured in months (a) What is the limiting value of the population'? (b) At what time (i.e., after how many months) will the populaton be equal to one half of the limiting value in (a)? Do not round any numbers for this part. You work should be all symbolic.) Problem #6(a): 10000000000 Enter your answer symbolically,...
3. A plant produces starch dependig on the intensity of heat it receives during the day. Assume the rate of starch production of the plant is 2 grams per hour dt +t where time t is measured in hours and S(t) is the amou noon each day (time t = o is noon, t-1 is 1pm and so on). of starch produced t hours after a. Estimate the tot al change in S(t) between 1pm and 3pm using the right-hand...
The size of a certain insect population at time t (in days) obeys the function P(t) = 400 0.00 (a) Determine the number of insects att=0 days. (b) What is the growth rate of the insect population? (c) What is the population after 10 days? (d) When will the insect population reach 560? (e) When will the insect population double? (a) What is the number of insects att=0 days? insects Enter your answer in the answer box and then click...
please answer 2d, 2e, and 2f and ahow all work.
The graph below represents the growth of a certain population. The population is in thousands and the time is in years. Use it to answer the following questions 2. 4 time a. What is the initial population? Use function notation to express your answer. b. What is the average rate of change in the population from year 2 to year 3? Illustrate on the graph above the line that shows...
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