Brain weight B as a function of body weight W in fish has been modeled by the power function B = 0.007W2/3, where B and W are measured in grams. A model for body weight as a function of body length L (measured in centimeters) is W = 0.12L2.53. If, over 10 million years, the average length of a certain species of fish evolved from 15 cm to 23 cm at a constant rate, how fast was this species' brain growing when the average length was 19 cm? (Round your answer to four significant figures.)

Q: Suppose that a room containing 1300 cubic feet of air is originally free of carbon monoxide (CO).…

A:

Q: The rate of increase of the population of a certain city is proportional to the population. In 1970,…

A:

Q: A teacher makes a cup of coffee. At 13:00 the coffee in the cup has a temperature of 86 Celsius and…

A: (a) It's given that the rate of cooling coffee is proportional to the difference between coffee…

Q: The half-life of palladium-100 is 4 days. After 20 days a sample has been reduced to a mass of 0.375…

A:

Q: The half-life of a certain radioactive substance is 12 hours. There are 8 grams present initially.…

A:

Q: In 1995, the rate of violent crimes in New York City continued to decrease, but at a slower rate…

A:

Q: The population, P, of a small city (in thousands) over time is given by the function P(t) 600t %3D…

A:

Q: Suppose that a room containing 1400 cubic feet of air is originally free of carbon monoxide (CO).…

A: The complete silutions are given below

Q: The rate of natural increase of the population of a certain city is proportional to the population.…

A:

Q: Strontium-90 is a radioactive material that decays according to the function A(t) = An e -0.0244t,…

A:

Q: The energy cost of horizontal locomotion as a function of the body weight of a marsupial is given by…

A:

Q: The energy cost of horizontal locomotion as a func- tion of the body mass of a lizard is given by E…

A: Given: E = 26.5m-0.34

Q: A teacher makes a cup of coffee. At 13:00 the coffee in the cup has a temperature of 86 Celsius and…

A: Given that the initial temperature of the coffee is 86° Celsius and the air temperature of the room…

Q: "Brain weight B as a function of body weight W in fish has been modeled by the power function B =…

A: Given B=0.007W2/3 ....(1)  ,where B is the Brain weight and W is body weight. and W=0.12 L2.53…

Q: 4. Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The…

A: Given that the model for the concentration of the antibiotic in the sinus cavity as a function of…

Q: Strontium-90 is a radioactive material that decays according to the function A(t) = Ao e ', where A,…

A:

Q: The growth in the number​ (in millions) of Internet users in a certain country between 1990 and 2015…

A: The logistic function is given as, , where G0=initial number m= maximum possible number t=time…

Q: The number of bacteria in a culture was initially 8000 and it was 12,400 after 2 hours. find a…

A:

Q: A college dormitory houses 100 students, each of whom is susceptible to a certain virus infection. A…

A: This is a problem of modeling and IVP.

Q: The half-life of uranium-135 is 60 years. Suppose we have a 20 gram sample. 1. Find a function…

A: Given:- The half-life of uranium-135 is 60 years. Suppose we have a 20 gram sample. To find:- 1.…

Q: 54. U.S. Citizens 65 Years and Older The number of U.S. citizens aged 65 years and older from 1900…

A: The growing rate is given by: R(t)=0.063t2-0.48t+3.87   (0≤t≤15) million people/decade, where t is…

Q: A population of bacteria is initially 3900. After 4 hours the population is 1300. If this rate of…

A:

Q: A hot air balloon launches straight up into the air from the top of a hill with an elevation of 200…

A: Given time=t, elevation = E Given that at t=0 minute, h=200 feet At t=20 minute, h=620 feet So two…

Q: Brain weight B  as a function of body weight W in fish hasbeen modeled by the power function B=…

A: Given Substitute for W in first equation, we get Let t be time in millions of years.…

Q: The size P of a certain insect population at time t​ (in days) obeys the function P(t)=400e0.07t.…

A:

Q: The carbon monoxide level in a city is predicted to be  0.02x3/2 + 1 ppm (parts per million), where…

A:

Q: Suppose that a room containing 1500 cubic feet of air is originally free of carbon monoxide (CO).…

A: To find the solution

Q: When organic matter is introduced into a body of water, the oxygen content of the water is…

A: We have, Pt=1-12t+12+144t+122=1-12t+12-1+144t+12-2 By taking derivative of the function with respect…

Q: 54. U.S. Citizens 65 Years and Older The number of U.S. citizens aged 65 years and older from 1900…

A:

Q: The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is…

A:

Q: Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The antibiotics…

A:

Q: Brain weight B as a function of body weight W in fish has been modeled by the power function B =…

A: Given that,

Q: The cost of an appliance whose purchase price is $600 and annual hydro cost is $115 is given by the…

A:

Q: A bacteria colony grow at a rate of 11% per year. If the initial sample has a mass of 500 grams,…

A: Solution:- function is missing in the question , but according to formula i have solved the…

Q: Strontium-90 is a radioactive material that decays according to the function A(t) = Ao e -0.0244t,…

A: Given : a.   Decay rate = -0.0244= -0.0244×100%= -2.44 %

Q: On wet roads, under certain conditions the front tires of a car will hydroplane, or run along the…

A: Step:-1 Since, given that V as a power function of p and p V 25 52.5 30 57.4 35 62.0 40…

Q: The population of Minnetonka, Minnesota is given as a function P (t) = 40e' e0.02t where P(t) is…

A:

Q: The half life of substance A is 22 years, and substance B decays at a rate of 30 % each decade. (a)…

A:

Q: A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the…

A:

Q: = a A person's intelligence quotient (IQ) is measured by the function I(m, a) = 100m where a is the…

A: This question can be solved using the concept of rate of change of quantities.

Q: A ball is thrown straight down from the top of a 300-ft building with an initial velocity of -12 ft…

A: We need to find the velocity after 4 seconds

Q: Strontium-90 is a radioactive material that decays according to the function A(t) = A e -0.0244t,…

A:

Q: 1. A truck that delivers essentials in remote areas can travel 85 kilometers. Which of the following…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: The time rate of change of a rabbit population is proportional to P^(3/2) . At time t= 0 days, the…

A: Please see the below picture for detailed solution.

Q: The average daily metabolic rate for captive animals from weasels to elk can be expressed as a…

A: Given- r=140.2m0.75 To find- drdt and determine drdt when the gaining mass at a rate of 2 kg per…

Q: Suppose the average daily metabolic rate for certain types of animals can be expressed as a function…

A:

Q: The population of a colony of mosquitoes obeys the law of uninhibited growth.(a) If N is the…

A: Since The population of a colony of mosquitoes obeys the law of uninhibited growth.  (a) If N is the…

Q: On a desert island lives a colony of extremely active dormouse. The population are given by time t…

A: function of population by the time t(in months) is given by y(t)=10004+t-12πcosπ6t Table for the…

Q: Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of…

A: Given query is to find the volue at time t

Q: 2. In a community of 10000 people, the rate at which a rumor spreads is jointly proportional to the…

A: Let ‘n’ be the number of people who have heard the rumor 10000-n be the number of people who have…

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.