Model the following data using an exponential function of the form f(x) = Ab^x . set up a system of equations, and solve it to get A and b.  (a) f(x) is exponent

Q: Suppose 15 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

A: Please refer the attached image for complete solution.

Q: The radioactive isotope of lead Pb-209, decays at a rate proportional to the amount present at any…

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

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Q: A certain radioactive element decays over time according to the equation where 4= the number of…

A: Solution attached below

Q: Suppose 30 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

A: We have the following data : Initial number of plants = 30 Spreading rate = 80% a month Carrying…

Q: Ununoctium decays naturally at the rate proportional to the original quantity. If there are 20 grams…

A:

Q: the countries of russia  and  armenia each had  populations of 5.5 million in the  year…

A: Given Information :  The countries of Russia  and  Armenia each had  populations of 5.5 million in…

Q: An fruit grower knows from previous experience and careful data analysis that if the fruit on a…

A: *Concept:- first form Revenue equation in terms of number of weeks (x). then, use maxima principle,…

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A: To use the given data (exponential model) to determine the initial data

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A: Let height of triangle = h Base = b Then, we are given that:

Q: Suppose 275 trout are seeded into a lake. Absent constraint, their population will grow by 75% a…

A: Given problem Given that   Suppose 275 trout are seeded into a lake. Absent constraint, their…

Q: Suppose 175 trout are seeded into a lake. Absent constraint, their population will grow by 45% a…

A: At initially 175 trouts are present,Population will grow by 45% a year,Maximum trouts which can be…

Q: population doubles in size every 29 years assuming exponential growth, find the a. annual growth…

A:

Q: If there are 520 grams of Tadioactive material with a half-life of 12 hours, how TIuch of the…

A: The material is decaying at a constant rate, every 12 hours it is getting halved.  So, it is an…

Q: Plot the percentage of machines not running as a function of the service factor for a population of…

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Q: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: Suppose 150 trout are seeded into a lake. Absent constraint, their population will grow by 35% a…

A:

Q: An fruit grower knows from previous experience and careful data analysis that if the fruit on a…

A: TO FIND: How many weeks should the grower wait before harvesting the apples in order to maximize the…

Q: Suppose 225 trout are seeded into a lake. Absent constraint, their population will grow by 60% a…

A: Since the growth rate is given in terms of percentage for first of all we will convert into decimal…

Q: Suppose 175 trout are seeded into a lake. Absent constraint, their population will grow by 60% a…

A: Recall: Logistic growth model   P(t)=m1+m-PPe-ktWe have, P=175, m=2000, k=60%=0.60, t=5 years

Q: An fruit grower knows from previous experience and careful data analysis that if the fruit on a…

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Q: A small newspaper company is downsizing and has lost employees at a steady rate. Twelve months ago…

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Given that increasing altitude of the triangle dh=2cm/min The increasing area of the triangle dA =…

Q: An fruit grower knows from previous experience and careful data analysis that if the fruit on a…

A: The average pounds of fruits is 130 pounds, and the selling price is $0.6 per pound. The yield per…

Q: Another quantity has initial value of 400 and decays at a rate of 5.2% per hour. Give an exponential…

A: Let the function be fx=400ax     ....(1) After 1 hour  fx=400-400×5.2100      =400-20.8=379.2

Q: Suppose 16 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

A: Here we have to use the logistic growth model. I have appended the formula used in the solution part…

Q: Explain a general mathematical modeling to growth of Human population. And what will be the Iraq…

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Q: A radioactive substance decays at a continuous rate of 17% per day.  After 8 days, what amount of…

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Q: Suppose 275 trout are seeded into a lake. Absent constraint, their population will grow by 50% a…

A:

Q: In 1986 the Chernobyl nuclear power plant exploded, and scattered radioactive material over Europe.…

A: NOTE: Refresh your page if you can't see any equations. . let the initial amount of cesium-137 is…

Q: A man with ​$30,000 to invest decides to diversify his investments by placing ​$15,000 in an account…

A: Total Amount = $30,000Amount  compounded continuously =  Pertand   Amount compounded  Anually…

Q: From the early 1980's through 2012，the number of adults enrolled in Bachelor's Degree programs has…

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Q: Suppose 175 trout are seeded into a lake. Absent constraint, their population will grow by 65% a…

A:

Q: A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A…

A: Linear equations

Q: If in the year 2000 there were 1.26 million metric tons of beef produced and demand is growing at a…

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Q: Suppose 200 trout are seeded into a lake. Absent constraint, their population will grow by 70% a…

A: Given problem:- Suppose 200 trout are seeded into a lake. Absent constraint, their population will…

Q: The accompanying table shows the number of bacteria present in a certain culture over a 4 hour…

A: From given data, X Y X*Y X*X 0 90 0 0 1 103 103 1 2 109 218 4 3 129 387 9 4 141 564 16…

Q: When do we use the Chain rule in derivates of exponential function

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Q: An fruit grower knows from previous experience and careful data analysis that if the fruit on a…

A: To find: How many weeks should the grower wait to maximise the sales revenue per tree.  Find the…

Q: The polluted water from Pond 1 drains into Pond 2 at 8 gallons per minute. Pond 1 initially contains…

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Q: How is the slope coefficient interpreted in a log-linear model, where thedependent variable is (i)…

A: The slope coefficient interpreted in a log-linear model of the dependent variable is given below as,…

Q: Aman with $30,000 to invest decides to diversity his investments by placing $15,000 in an account…

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Q: The following table gives the total number of U.S adults with diabetes for selected years from 2010…

A: Hi! You have posted multiple subparts. As per the norm, we will be solving the first three subparts.…

Q: If a village has a population of 2000 and a natural growth rate of 3.7% but has a carrying capacity…

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Q: Initially 100 millions of radioactive substance was present. After 6 hours the mass has decreased by…

A: Given query is to find the amount of radioactive substance after 24 hours.

Q: Find: > LSRL equation and predict the number of hours of walk per week for 35-year old person > r…

A: The independent variable is Age. The dependent variable is Hours of walk per week. This is simple…

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Q: Suppose 19 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

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Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

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Q: Can someone help me create a linear, exponential, or polynomial equation that would model the…

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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.