A 500 gallon oil spill undergoes a cleanup process. The company hired to clean the spill can remove 15% of the reaining oil each week. Find a formula to express the total oil left, C, as a function of time t in weeks since the oil spill occurred.

Q: The population of bison in Canada was found to have a growth rate of  20%. If the If the population…

A:

Q: Number of bacteria in a rapidly growing culture was estimated to be 10,000 at noon, 40,000 after…

A:

Q: The number of bacteria in a culture is given by the function ?(?) = 350?^0.8?, where t is measured…

A:

Q: Adam puts $800.00 into an account to use for school expenses. The account earns 15% interest ,…

A:

Q: One yardstick for measuring how steadily-if slowly-athletic performance has improved is the mile…

A: (a).       The function that express the record time for the mile run, M, in terms of number of…

Q: Q2: The population of a state is known to grow at a rate proportional to the number of people…

A: Given- The population of a state is known to grow at a rate proportional to the number of people…

Q: he amount of a certain radioactive substance decreases by 15% every hour. If a sample starts with…

A:

Q: The function represents the rate of flow of money (in dollars per year) over the given time period,…

A: Given that, The function of future value is  f(t) = 2000  rate, r = 3% = 0.03 time , t = 3 years  To…

Q: Fifty percent of the amount of a certain drug is eliminated from the body every hour. A 500mg drug…

A: Given that, Fifty percent of the amount of a certain drug is eliminated from the body every hour…

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

A:

Q: Logan invests $4000 at an annual interest rate of 6%.How much money will she have after 10 years if…

A:

Q: Find a formula for the exponential function passing through the points (-1,-) and (1,8) y% =

A:

Q: Assume that a runner runs a 100 meter sprint in 12.3 seconds. He accelerates steadily in the first…

A: The runner accelerates steadily in the first 25 meters. Let the acceleration be a m/s2 and suppose…

Q: Experimentally, the number of bacteria in cultivation duplicates for each hour. If there are 1000…

A:

Q: A total of $50000 is invested, part of it at 5% and the rest at 7.5%. The totalinterest after one…

A:

Q: An oral medication is absorbed into the bloodstream at the rate of 3e−0.04t milligrams per minute,…

A:

Q: An investment earning interest at the rate of 10%, compounded continuously, will double in tyears.…

A: Let's solve,

Q: new

A: Please refer to the image below

Q: Since January 1980, the population of the city of Brownville has grown according to the mathematical…

A:

Q: In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the population had…

A: Given,           In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the…

Q: The rate of growth of sales (sales per day) for a particular company is predicted to be 35e0.012,…

A:

Q: Find a formula for the exponential function passing through the points (-3,- -) and (2,32) 32 y =

A: The standard form of exponential function is given below: y=abx where, a≠0, b>0 and b≠1.

Q: Find a formula for the exponential function passing through the points (-2,-) and (1,10) y =

A: On solving this we will asume firstly general exponential function so  we will get

Q: The gross domestic product, G, of Switzerland' was 685.4 billion dollars in 2013. Give a formula for…

A:

Q: Use the fact that the world population was 2560 million in 1950 and 3040 million in 1960 to model…

A:

Q: Find a formula for the exponential function passing through the points (-3, 2 / 27) and (1, 6). y =

A:

Q: The rate of growth of sales (sales per day) for a particular company is predicted to be 25e0.00r,…

A:

Q: Annual oil production for a region was about 520 million tons in 1950. Production increased at a…

A: Given that, Annual oil production for a region was about 520 million tons in 1950. Production…

Q: The rate of growth of sales (sales per day) for a particular company is predicted to be 25e0.067…

A:

Q: st rate. Consumers react to this rise ding today and spending tomorrow er, and he decides to…

A: The optimal choice for the Lili is shown below as,

Q: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly heating…

A: The insulation costs for the two bedroom  home is $2400.The costs of monthly heating in present…

Q: The population of Weston is currently 7,000. But the population is shrinking according to the…

A:

Q: A population of cattle is increasing at a rate of 100 + 20t per year, where t is measured in years.…

A: Given : A population of cattle  is increasing at the rate of 100+20t per year

Q: determine the time neeessary for P dollars to double when it is invested at interest rate r…

A:

Q: The population of the United States is predicted to be P(t) = 310e0.0073t million, where t is the…

A:

Q: Juliana invested $5,000 at 5.25% p.a. simple interest. How many days will it take for her investment…

A:

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

A: An oral medication is absorbed into the bloodstream at the rate of 7e-0.04t.

Q: a) What is the maximum amount of the salt that will ever dissolve in the methanol? b) If x = 50 when…

A:

Q: The Population of Barangay Siksikan is increasing at a rate proportional to its current population.…

A: ⁎ Given:        The population of Barangay Siksikan i.e, increasing     at a rate proportional to…

Q: Water is pumped out of a holding tank at a rate of 3-3e-0.5t liters/minute, where t is in minutes…

A:

Q: The rate of change of the income produced by a business selling face shields is given by f(t) =…

A:

Q: Biologists stocked a lake with 600 fish and estimated the carrying capacity to be 7400. The number…

A: The form of the logistic equatIon is: y(t)=c1+aebt The carrying capacity is: 7400 Therefore c = 7400

Q: A factory bought a machine a certain number of years ago, and the value of the machine depreciated…

A: here we took rate as negative because it is given as depreciation.

Q: The table gives the profit, P of a fast food chain, where P is in millions of dollars and t is in…

A: Given,

Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We can find the answer as below.

Q: After 12 hours, half of a 16 gram sample of a radioactive element remains. Find the constant k for…

A:

Q: In 1990 (t = 0), the world use of natural gas was 74709 billion cubic feet, and the demand for…

A: Explained below

Q: In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Solve,…

A: Given: In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million

Q: Find a formula for the exponential function passing through the points (-1,3232) and (1,6)   Y= ?

A:

Q: if $2000 is invested at 5%, compounded continuosly for t years, the value, A of the investment is…

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.