The number of people in a community who became infected during an epidemic t weeks after its outbreak is given by the function f(t)= 10,000/(1+ae-kt) where 10,000 people of the community are succeptible to the disease. Assume that 5000 people were infected initially and 8984 had been infected by the end of the fourth week.  How many people were infected after 8 weeks?

Q: Find the interval on which the graph of f(x)=ln(x^2+1) is concave upward ?

A:

Q: If an archer shoots an arrow straight upward with an initial velocity of 160ft/sec from a height of…

A: If the arrow reaches the ground then h(t)=0…

Q: Find f'(1) for f(x) = ln(3x² – 6x – 2) rounded to 3 decimal places. f'(1) = |6-6x/3x^2-6x-2

A:

Q: Consider the following function. f(x) = −x2 − 6x − 6 Find its average rate of change over the…

A: Solution : According to the question,     The average rate of change of the function f(x) over an…

Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following…

A:

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

A:

Q: A culture of bacteria is known to grow at a rate proportional to the present amount. After one hour…

A:

Q: Find the domain of the function. f(x) = ln(x^2 + 1)

A: Definition used:The domain of a function is the complete set of possible values of the independent…

Q: Find the interval/s where the function is increasing and where it is decreasing: f (x) = x³ – 3x + 3…

A:

Q: Use this formula to find the instantaneous rate of change of the function at the given x-value.f(x)…

A: Given function is

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

A:

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

A:

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: As population is proportional to present population. So we need to form a differential equation. and…

Q: The population of a certain country is known to increase at a rate proportional to the number of…

A: Solve by making differential equation

Q: Determine if the MVT applies to the function on the given interval. If so, find the points that are…

A:

Q: Suppose f(x)=6x2+9x−13. Write an expression in terms of x and h that represents the average rate of…

A: Average rate of change is ratio of change in function values and time interval.

Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following…

A:

Q: Differentiate. f(x) = - 2 e -X t'(x) = ]

A:

Q: 1. Given the function f(x) = Vx5 – 3Vx², find the interval(s) of increase.

A:

Q: 2. Consider a population of bacteria that grows according to the function f(t)=500e^0.05t , where t…

A:

Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: Suppose we have a tank that contain 10 litres of water and 50 g of salt. The salt solution is…

A: given , tank that contain 10liters of water and 50 gram of salt .  so , initial concentration =>…

Q: Find the domain of the function: h(x) = ln x2

A: h(x)=ln x2

Q: Find the domain of the function: f(x) = ln(4 - x)

A: we have to find the domain of the given function. f(x)=ln(4-x)

Q: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 400-cc organ at a rate of 5…

A:

Q: When $1000 is invested at r% interest (compounded continuously) for 10 years, the balance is f (r)…

A: Consider that $1000 is invested at r% interest compounded continuously for 10 years. Calculate the…

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: We have to find the differential equation for the population growth.

Q: A 2000-liter cistern is empty when waterbegins flowing into it (at t = 0) at a rate (in L/min) given…

A: It is given that   . Suppose a quantity Q changes over time at a known rate Q'. Then the net change…

Q: A mass of 200 grams of a particular radioactive substance decays according to the function m(t) =…

A: To find when does the mass reaches 50 grams

Q: Suppose the rate at which consumers purchase peanut butter is increasing at a rate given by  f ′(t)…

A:

Q: In certain conditions, the atmospheric pressure (p) in the height (h) is given by p=29e-0.000034h.…

A: It is given that the atmospheric pressure in the height is given by the function…

Q: A mass of 100 grams of a particular radioactive substance decays according to the function m(t) =…

A:

Q: The population, f, of a small community on the outskirts of a city grew rapidly over a fifteen year…

A: Newton's backward difference formula uses the formula below to approximate f(x) .…

Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

A:

Q: A company has found that its rate of expenditure​ (in hundreds of​ dollars) on a certain type of job…

A:

Q: Find f''(x) for: f(x)=ln⁡x/4x

A:

Q: Given f(x)=ln(5x), what is f'(x) when x=14.2?

A:

Q: 2. Determine the zeroes of 2 x² = x f(x) instantaneous zeroes using a table of values. — 3x 4 and…

A: To find the zeroes of the polynomial.

Q: Suppose a survey shows that a mayoral candidate is gaining votes at a rate of 2100t + 1500 votes per…

A:

Q: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

A:

Q: A 7,986-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

A:

Q: For the function given by g (x)= x² + 2x +1, find the average rate of change of function over the…

A: We will find the average rate of change of function as following.

Q: A tank with a capacity of 300 litres initially contains 150 liters of pure water. Brine contains 3gm…

A: Solve the question 1 Capacity of tank=300litres Amount of pure water in tank initially=150litres…

Q: Find a good numerical approximation to F(4) for the function with the properties that F'(x) = e-x+15…

A:

Q: Use the second derivative to determine f"(3) for the function f(x) = x² In (x) 2ln(3) +2 O 3ln(2) +3…

A: topic - derivatives

Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?

A: average rate fo change in an interval (a,b) =f(b)-f(a)b-a

Q: A ball is thrown upward so that its height above the ground after time t is h(t) = 20t-5t, where h…

A: Given is : We have to find time when h(t) or height will be maximum And for height , function is :…

Q: Consider the following function. f(x) = -x2 - 10x – 9 Find its average rate of change over the…

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.