The weight Wt of radioactive uranium after t years is given by the formula Wt =  W0 × 2−0.0002   grams,  t ≥ 0. Find a. the original weight b. the percentage of weight loss after 1000 years.

Q: √t 12. If a factory continuously dumps pollutants into a river at the rate of tons per day, then the…

A:

Q: The voltage from an alternating current generator is given by V(t)=160cos120πt,where t is measured…

A:

Q: If   C(t)=45.5te^−0.21t measures the​ concentration, in ng/ml​, of a drug in a​ person's system t…

A:

Q: The weight, M, of an astronaut on the moon is directly proportional to the weight, E, on Earth. An…

A: Weight on moon will be 12 Kg.

Q: It is known that a substance turns into another substance as a result of a chemical reaction. The…

A: Given that the conversion rate of a substance is proportional to the amount of substance present.…

Q: A model for the basal metabolism rate, in kcal/h, of a young man is given by the formula below,…

A: The total basal metabolism is given by, ∫024R(t) dt

Q: Each side of square is increasing at rate of 4 cm/s. At what rate is the area of the square…

A:

Q: For an average person, the rate of change of weight W (in pounds) with respect to height h (in…

A: Given: The rate of change of weight W (in pounds) with respect to height h (in inches) is…

Q: The value V of a jet ski t years after it was purchased can be estimated using V(t)= 3,795/t +610…

A: Given that The value V of a jet ski t years after it was purchased can be estimated using V(t)=…

Q: The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. a) What is the…

A: Applications of derivatives

Q: The side of a cube increases at the rate of 3 m/s, when side of the cube is 8m . Then the rate of…

A:

Q: A factory produces bicycles at a rate of 95 + 0.2t2 – 0.5t bicycles per week (t in weeks). How many…

A:

Q: The value of a machine, V, at the end of t years is given by v=C(1-r)t, where C is the original cost…

A: Consider the function for machine value: v=C1-rt v=Future valueC=Original costr=Ratet=Time

Q: A bacterial population starts with 400 bacteria and grows at a rate of r(t) = (450.264)el.12567t…

A: as per bartleby guidelines i can do only first question .please ask other part separately.

Q: of children who can speak in at least single words by the age of t months can be approximated by the…

A: Given that t=14  We have to find p at t=14

Q: the velocity of a sky diver t seconds after jumping is given by v(t)=80(1-e^-0.2t). after how many…

A:

Q: A radioactive substance follows A(t) = 500(0.87)^t , where t is in months and A(t) is in grams. How…

A: Given that: A(t)=500(0.87)t, where t is in months and A(t) is in grams.

Q: The rate of change of N is inversely proportional to N². IfN (0) = 4, and N(2) = 6, what is N(5)? O…

A: The rate of change of N is inversely proportional to N2N(0)=4 and N(2)=6

Q: Assume y(t) = 100e0.05t. By (exactly) what percentage does y increasewhen t increases by 1 unit?

A: Given yt=100e0.05t Now, when t is increases by 1 unit then, yt+1=100e0.05t+1=100e0.05t·e0.05…

Q: where p(t) is the proportion of the population that knows the rumor at time t and a and k are…

A:

Q: As a cure to the epidemic that spread in the whole country, the Department of Health (DOH) released…

A: Method of substitution is used to find the value of a function at a particular point. For example…

Q: The weight Wt of radioactive uranium after t years is given by the formula Wt =  W0 × 2−0.0002…

A:

Q: Q3: Find the value of B, the energy density and the rate of energy flow per unit area S, for the…

A: Energy Density is defined as the total amount of energy in a system per unit volume.   It is denoted…

Q: c) What happens to the pH level of a mouth as the time since eating the sugary food increases?

A: answer is in step 2

Q: When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the…

A:

Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: Given expression is D=3000.98t where D is the temperature difference between the oven and the potato…

Q: For a substance C, the time rate of conversion is proportional to the square of the amount of…

A: Given: For substance C, the time rate of conversion is proportional to the square of the amount of…

Q: we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: GivenInitiall potato temp = 75° oven temp = 375°difference = 375-75difference =300°D = 300 x 0.98tD…

Q: If the radius and height of a cone grow1.8% and 2.0% from its original value, respectively,…

A: Let the radius of the cone be 1 unit. Then height of the cone is h=21=2 units. The volume of cone is…

Q: Cameron prepared 16 kilograms of dough after working 4 hours. How many hours did Cameron wörk if he…

A: We are given to assume linear relationship between time and amount of dough prepared

Q: A body of gas is contained in a vessel of volume v; the pressure is given by the formula ? = k/v .…

A: We will differentiate p=k/v with respect to time to get desired relationship between rate of change…

Q: A factory produces bicycles at a rate of 100+0.3t^2−0.5t bicycles per week (t in weeks). How many…

A: A factory produces bicycles at a rate of

Q: If   C(t)=55te^(−0.2t) measures the​ concentration, in ng/ml​, of a drug in a​ person's system t…

A: A function is a rule that is used to associate a number to a particular point.  If y=C(t) is a…

Q: Use the model given to answer the question about the object or process being modeled.

A: Given- P=14.7+0.45d To make- (a) A table that gives the pressure for each 10 feet change in depth ,…

Q: The height, h, in meters of a dropped object after t seconds can be represented by h(t) = – 4.9t +…

A:

Q: he radius of a circle is increasing at a rate of 2 ft/min. At what rate is its area changing when…

A: Area of the circle , A =πr2, where 'r' is the radius of the circle.

Q: The rate at which yeast cells multiply is proportional to the number present. If the original number…

A: Given, The rate at which yeast cells multiply is proportional to the number present. the original…

Q: If MST = 200 and F = 1.04 what is MSE equal to? Only round final answer to 2 decimal places.

A:

Q: If the amount of drug in a person's blood after t hours is  (t) = t/(t2 + 25), when will the drug…

A:

Q: The water level in a tank decreases with time according to the following equation: h(t) = 1.8 t² –…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: * A hard-boiled egg at 97°C is put into a sink of 15°C water. After 5 minutes, the egg's is 35°C.…

A: Newton's cooling law is used

Q: As y increases by 10,x Jncreases by 5. Which equation represents this rate of change? (7.1B, 7.1D,…

A: Rate of change = change in y /change in x

Q: an oral medication is absorbed into the bloodstream at the rate of 5e^-0.4t milligrams per minute…

A: Given: An oral medication is absorbed into the bloodstream at the rate of 5e-0.4t milligrams per…

Q: At a constant temperature of 15ºC, the barometric pressure can be approximated by the formula…

A: At a constant temperature of 15ºC, the barometric pressure can be approximated by the formula…

Q: An oral medication is absorbed into the bloodstream at the rate of 7e−0.04t milligrams per minute,…

A: Find the equation for the rate at which the oral medicine is being observed. Then integrate the…

Q: The concentration C of a certain drug in a patient's bloodstream t hours after injection is given by…

A:

Q: Tom works for a constant hourly wage of w dollars. Which choice shows the correct relationship…

A: Tom's total earning of the week = e total no of work hours = h wage per hour = w

Q: A car traveled 50 miles in 40 minutes. Assume that the car will continue at this constant rate of…

A: Option (C) M=75 h is correct.

Q: If C(t) = 71.6t e -0.4t ng of a drug in a person's system t hours after the drug is administered,…

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.