A fish population oscillates 40 above and below average during the year, reaching the lowest value in January. The average population starts at 800 fish and increases by 4% each month. Find a function that models the population, \displaystyle PP, in terms of months since January,

Q: Express the gross salary G of a person who earns $14 per hour as a function of the number x of hours…

A: Given: Earning per hour = $14       To determine: Gross salary as a function of the number of…

Q: . Sketch the graph of the amount of a particular brand of coffee sold by a store as a function of…

A: To Sketch The graph of the amount of a particular brand of coffee sold by a store as a function of…

Q: The graph of the function fx) =/x is stretched vertically by a factor the transformed function…

A: Given- The graph of the function fx = x is stretched vertically by a factor of a and is translated 3…

Q: Differentiate between Increasing and Decreasing Functions?

A: If the value of the function, f(x) increases as the value of the x increases on an interval, then…

Q: Find the maximum rate of change of f at the point (1, 2). -2/2 2/2 4 -4

A:

Q: What is the common way to obtain a new function from an existing one?

A:

Q: FX) = Secx

A: Given function to be differentiated is : F( X ) = sec X2 In order to differentiate above function,…

Q: The value of a brand new car is $36, 000 and the value depreciates 15% every year. Write a function…

A: Please refer to the image below

Q: According to the National Center for Health Statistics, in 1990, 28% of babies in the United States…

A:

Q: When two odd functions are multiplied, the combined function is also an odd function.     True or…

A: Given statement is, when two odd functions are multiplied, the combined function is also an odd…

Q: An object is projected upward from ground level with an initial velocity of 500 feet per second. In…

A: velocity is the rate of change of position over time is velocity, calculated by dividing distance by…

Q: Give an example to explore numerically how a function behaves near a particular point at which we…

A: Solution: Consider y = f(x) = 1/x is the function Since at x = 0, this function is going to be…

Q: The initial weight of a container is 6.2 pounds. As water is added to the container, the weight…

A:

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: A bathtub that intially holds 65 gallons of water starts draining at rate of 8 gallons per minute.…

A: Construct a function for the number of gallons of water W (t) in the tub after t minutes of draining…

Q: Define Increasing and decreasing function?

A: According to the question, we have to define the increasing and decresing function. To check the…

Q: This describe the value of a function as approaches to some value?

A: Since we know that limit of a function f(x) as x approach c, f(x) approaches x as approaches c.

Q: Identify the open intervals where the function is changing as requested. Decreasing

A: We have to find the interval where the function is decreasing.

Q: create a piecewise function showing the rate of money f(x) that must be paid by a customer after…

A: In this question, First, we are to create a piecewise function showing the rate of money f(x)  that…

Q: 3. A toy company can make a doll worth Php55 for the Christmas season. If the production manager…

A: Given query is to find the profit function p(x) .

Q: anita is on a competetive rowing team . after 2 minutes the team rows at a constant speed of 4…

A: By making differential equation between distance and time

Q: during typhoo Ambo, PAGASA tracks the amount of accumulating rainfall. For the first three hours of…

A: For first three hours, the rain fell at a rate of 25 mm per hour.  So for time 1≤t≤3 the rate was 25…

Q: What are the Piecewise-Defined Functions?

A: Piecewise function is a function which has multiple sub-functions. Each sub-functions has different…

Q: Describe the relationship of input and output values for composite functions

A: Use the definition of composition of two functions.

Q: Suppose an insect population increases by a constant number each month. Explain why the number of…

A: Given : An insect population increase by a constant number each month.

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

A:

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: A man drives from Detroit to Chicago, say 300 mi., at an average speed of  60 mi. per hr., stops 1…

A: A man drives from Detroit to Chicago, say 300 mi., at an average speed of 60 mi. per hr., stops 1…

Q: What is the function of the graph in the image?

A:

Q: Since the beginning of the year, the price of a bottle of soda at a local discount supermarket has…

A: According to the given information it is required to express the price of the soda as a function of…

Q: Define the term constant function.

A: The constant function is defined as the function whose all domain value maps into a single value in…

Q: a technician earns a salary of 37200 plus $40 for each hour of overtime worked. Write a function to…

A: Let y be the total salary of the technician and x be the overtime worked hours.Then amount he will…

Q: Since the beginning of the year, the price of a bottle of soda at a local discount supermarket has…

A: Let P0 be the price of a bottle of soda at a local discount supermarket at the beginning of the…

Q: 2. During typhoon Ambo, PAGASA tracks the amount of accumulating rainfall. For the first three hours…

A: During typhoon Ambo, PAGASA tracks the amount of accumulating rainfall. For the first three hours of…

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: What is an even function?

A: we have to tell what is an even function.

Q: A function wherein all terms are of the same degree in terms of x and y is known as ________

A:

Q: 4. The regular adult admission price to an evening performance at a Cinema is Php 140.00, with the…

A:

Q: Find the points on the graph of the function that are closest to the given point. fx) %3D х2 - 3,…

A:

Q: 7. A worker gets $20/hour for a normal work week of 40 hours and time-and-a-half for overtime.…

A:

Q: The value of a brand new car is $10,000 and the value depreciates 19% every year. Write a function…

A:

Q: Sketch a rough graph of the function without using acalculator.   y=   -e-x

A: Given: y=-e-x

Q: Explain the Functions that are Nonlinear in the Parameters with example?

A:

Q: Describe an example of a real-live application of functions of two or more variables.

A:

Q: How can a function be described in pieces?

A: A function can be described in pieces with different formula in different intervals of its domain.

Q: Construct a function that is undefined at points 2,3 and π

A: We have to write a function fx which is not defined at the points x=2, x=3 and x=π. We know that a…

Q: Use function notation to represent that your annual salary after working five years at your job is…

A: We will find the required function as following.

Q: A rectangular plot of land will be fenced into three equal portions by two dividing fences parallel…

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.