In this exercise we explore further the Pacific sardine population. Studies to fit a logistic model to the Pacific sardine population have yielded the following. N=2.41+239e−0.338t Here, t is measured in years and N is measured in millions of tons of fish. (Round your answers to two decimal places.) (a) If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2 million tons? [Suggestion: One way to solve this is to make a new logistic formula using K = 2.4, r = 0.338, and N(0) = 0.05.] t = ____ yrs (I made a new formula and came up with: N=2.41+48e−0.338t, but using this is giving me all the wrong answers.) (b) The value of r used in the model for the Pacific sardine population ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year (with the carrying capacity still at 2.4 million tons). Answer the question in part (a) using this lower value of r. t = ____ yrs

Q: 2. An endangered species of fish has a population that is decreasing exponentially. The population,…

A:

Q: (d) Write a logistic differential equation that models the growth rate of the panther population.…

A: dPdt=0.5227P1-P420 P0=35

Q: Find a logistic function that satisfies the given conditions: y = 33 20 (0, 11) -20 (-2, 1) 20 40 2

A:

Q: The table lists the number of species of birds on islands of various sizes. Find values for a and b…

A: Given query is to find the value of a and b.

Q: The logistic model P(t) = OA. ⒸU. FU/ i5 te pervemage vi fiusenvius without a personal computer in…

A: The given equation isWhere t is the number of years after 1986 and P is the percentage of households…

Q: Which of the following is equivalent to 7% = a + 3? log(a+3) 7 = y log7 y = a +3 log, 7 = a +3 Ology…

A:

Q: The following are assumptions of the logistic model: No immigration or emigration а. O b. 1>1 No…

A: Logistic model is a type of continuous distribution. It has two parameters they are location and…

Q: Find a natural logarithm regression equation for the data in Table 1.16 and superimpose its graph on…

A: Year Cubic Feet(trillions 1997 5.76 1998 5.98 1999 6.26 2000 6.47 2001 6.60

Q: The population of a town is growing exponentially and can be modeled by the equation f (t) = 42 ·…

A: Put the values in given equation

Q: 1. Write down and describe the Logit model you would formulate in this case. 2. Estimating the model…

A:

Q: A population numbers 11,000 organisms initially and grows by 19.8% each year. (A) Suppose P…

A: (a) Given that, A population numbers is 11,000. The rate of increasing population is 19.8% per year…

Q: Question 8 Suppose 14 blackberry plants started growing in a yard. Absent constraint, the blackberry…

A:

Q: Calculate N(6) Round to the nearest whole number.

A: Simply putting t=6 in given expression of N we find the value N(6) as follows :

Q: The pH of a solution is given by the formula pH = log 10- in which H+ is the concentration of…

A: The pH of a solution is given by formulaWhere,  is the concentration of the hydrogen ions in gram…

Q: A breeding group of foxes is introduced into a protected area, and the population growth follows a…

A: Given Logistic Model: N=32.5+0.7(6)t  To find time t, when the fox population will reach 85

Q: You are asked to find the value of a certain number associated with the logistic formula K N = 1 +…

A:

Q: The variables and y have an exponential relationship, one of the form y=C.a². Suppose that we also…

A:

Q: Jared Shar Round answers to two decimal places. A study is done on the efficiency of wind turbines y…

A: We will find out the required value.

Q: Tutorial Exercise Radioactive radium has a half-life of approximately 1599 years. What percent of a…

A:

Q: Question 1 Researchers are studying which variables impacted survival of crew and passengers aboard…

A: The provided logistic regression model is as…

Q: An experiment involves dropping a ball and recording the distance it falls (y) for different times…

A: Here we are given a data and 4 scatter plots.  From which we have to choose the one that best fits…

Q: A population grows according to an exponential growth model. The initial population is Po = 15, and…

A:

Q: You are asked to find the value of a certain number associated with the logistic formula N =  K/ 1+…

A: Consider the given logistic formula.

Q: 7. Assume that the carrying capacity for a certain region is 800 million. The population was 282…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.