A bacteria colony initially has 4000 cells and triples every week. A function that can be used to model the population, p, of the colony after t days is A) p() = 4000(2) B) p(t) = 4000(3) p(t) = 4000(2) 7 D) p(t) = 4000(3) 7

Q: Which shows where the function is decreasing?

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A: Represent the required function as f(x). Observe carefully, the assumed domain and range for the…

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Q: i. Find the equation of a power function through the points (2, ) and (, 8). ii. Now, find the…

A: i) To find a power function through points 2,18 & 14,8. The power function is given by: y=axb

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A: Given function, f(x)=4x6-615

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Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.…

A: increasing and decreasing intervals of fucntion  fx=3x4 − 4x3 − 12x2 + 5

Q: A 400-room hotel can rent every one of its rooms at $120 per room. For each $1 increase in rent, two…

A:

Q: What are the expressions simplified and are the functionsinverses?

A: We will show that, both f°h and h°f are identity maps on their respective domain. Then, we can claim…

Q: A team of researchers finds that there is a relationship between the overall health of a forest…

A: Given function: fx=13x3+676x5+39 where, x is in tens of thousand of beetles. f(x) is thousands of…

Q: A 1 lb sponge initially contains 5 lb of water. As it is lifted up from the ground, the sponge loses…

A: Answer is option d here decrement in water is linearly (as constant rate)

Q: 1- Study the measurability of the functions:

A: Given  Two functions....we must study the measurability of the functions....where p is not…

Q: The percentage of gross domestic product​ (GDP) in a state going toward health care from 2007…

A: Given, the modelled function f(x) = 1.3lnx + 14.7, where f(x) is the percentage of gross domestic…

Q: The economic dependency ratio is defined as the number of persons in the total population who are…

A: The economic ratio is modeled by the function. Rx=-0.0002x3+0.052x2-4.06x+192

Q: A farmer decides to build a fence to enclose a rectangular field in which he will plant a crop. He…

A: Let width = x feet. Given perimeter=1400 and length = 100 feet. From there we find x.Answer(a): 600…

Q: How can we write a formula for this function?

A: The given function is a pair of two lines which are joined continuously. We will find the formula of…

Q: The equilateral trianhle is inscribed in a circle of radius 6r. Express the area A within the circle…

A:

Q: Suppose that Px represents the percentage of income spent on health care in year xand represents…

A: Given, P(x) represents the percentage of income spent on health in year x. I(x) represents income in…

Q: Life expectancy at age 65:  By using the Social Security Administration data for selected year from…

A:

Q: 18. Suppose that a company produces and sells bicycles and that the start-up cost is $3000 and $75…

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Q: A team of researchers finds that there is a relationship between the overall health of a forest…

A: We need to find maximum number by drawing graph.

Q: The construction industry was one of the hardest-hit by the recession of 2008, but housing starts…

A: NOTE: Refresh your page if you can't see any equations. . here x= number of years after 2002 so…

Q: The number of concurrent users of a social networking site has increased dramatically since 2001. By…

A: The function P(t)=2.8291.484t, where t is the number of years after 2001,models this increase in…

Q: What does it mean for a function to be defined implicitly by an equation?

A: An implicitly defined function is a function that is presented as the solution of some equation or…

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing. show…

A: Topic = Functions

Q: The number of concurrent users of a social networking site has increased dramatically since 2002. By…

A: The given function is Pt=2.4491.487t. t is the number of years after 2002. that is, t=0. Now, t is…

Q: A rancher wants to fence in an area of 1,500,000 square feet in a rectangular field and then divide…

A: Let the length of the rectangular field be y and the width be x. Assume the farmer divides the field…

Q: An articlet in The New York Times states, "The number of gas stations [in a city] grows only in…

A: We will use the given relation between population and gas station.

Q: of Zzyzx has been decreasing linearly for the past 7 years when the population was 2550. This year…

A: In this question, the concept of linear equation is applied. Linear Equation An algebraic equation…

Q: Based on past experiences, a homeowner estimates that appliances lose 35% of their resale value each…

A:

Q: A rancher wants to fence in an area of 500,000 square feet in a rectangular field and then divide it…

A: Let l be the length and w be the width of a rectangle.Then Area = l×b Perimeter = 2×(l+b)

Q: How would I find a function that models this?

A: From the given table , it is observed that the given table can represents a linear function.

Q: A 600 room hotel in Orlando is filled to capacity every night when the room price is $90  per night.…

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Q: A biologist has discovered that the weight of a certain fish is a power function of its length. He…

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Q: A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a…

A: Given h(t)= -4.9t^2+24t+8

Q: You have 1200 feet of fencing to enclose a rectangular region and subdivide it into three smaller…

A: Let  x and y be length and breadth of rectangular region respectively. Given data, Perimeter of…

Q: Supposed that from 2020 to 2060, the number of females in the U.S. under the age of 18, in millions…

A: Given Data: The number of females in the US under 18 is: N=0.140x+36.4 The slope of the graph of the…

Q: How can we Represent a Function Numerically?

A: A function f from a set A to a set B is a rule that associates every member of set A a unique member…

Q: The number of concurrent users of a social networking site has increased dramatically since 2001. By…

A: The given question has been solved in detail

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: It is give that population is N and G be the number of gas stations in a city related by G=cN0.77.…

Q: Express the area A of a rectangle as a function of the length x if the length of the rectangle is…

A: The area of the rectangle is given by the formula A=l×w where l is the length of the rectangle and w…

Q: A ball is thrown in the air from the top of a building. it’s height,and meters above ground,as a…

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Q: Solve no 73

A:

Q: An articlet in The New York Times states, "The number of gas stations [in a city] grows only in…

A: given that G=cN0.77

Q: You have 600 feet of fencing to enclose a rectangular field. However, one side of the field lies…

A: To Determine: Express the area of the field, A, as a function of one of its dimensions, x. Given:…

Q: The population of Boston, MA in 2019 was 692,600 people with an annual rate of increase 1.4%. In…

A: Given the function of population grows is P(x) = 692,600·1.014x where x is number of years. We have…

Q: A biologist has discovered that the weight of a certain fish is a power function of its length. He…

A:

Q: A ball projected upwards with a velocity of 128 feet per minute from a Height of 5 feet above the…

A: Ball reach its maximum height at t = 4 minutes

Q: You have 800 feet of fencing to enclose a rectangular field. However, one side of the field lies…

A: Rectangular field: You have 800 feet of fencing to enclose a rectangular field. One side of the…

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.