A certain type of bacteria is known to grow at the rate proportional to square root of the amount that is present. If you start with 3 grams of the bacteria and in two hours there are 3.5 grams, how much you will have after 7 hours ?

Q: The amount of pain reliever in tony's bloodstream decreases at a rate that proportional at any time,…

A: Given: amount of medication taken initially =  180 milligrams The amount of medication is halved…

Q: The length of the rectangle is decreasing at a rate of 5 centimeters per second, and its width is…

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Q: The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a…

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Q: A population of mosquitoes increases at a daily rate of 1/2 times the current population. You can…

A: Given that A population of mosquitoes increases at a daily rate of 1/2 times the current population.…

Q: The length of the rectangle is decreasing at a rate of 5 centimeters per second, and its width is…

A:

Q: Two cars are initially 1000 miles apart on a road that runs East/West. Car A drives 40 miles per…

A: To determine the rate of change of distance between two cars after 10 hours and 20 hours of travel.

Q: The mass of a cube in grams is M=x^3+0.1x^4, where is the length of one side in centimeters. If the…

A:

Q: In the absence of predators the population of mosquitos in a certain area would inccrease at a rate…

A: Let P(t) be the population of mosquitoes in the area with t in weeks, and k be the rate at whichthey…

Q: A tank contains 2,000 L of brine. Brine containing 5 kg/L of salt flows in at 10 L/min, and the…

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Q: A substance cools in moving air at a rate proportional to the difference between the temperature of…

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Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: Model the given problem dpdt=kp if p is the present number of bacteria integrate it on both sides…

Q: A population of bacteria grows at a rate proportional to the number of bacteria at the time. There…

A: Given that:                      Bacteria growth rate is proportional to the number of bacteria at…

Q: certain culture of bacteria, the rate of increase is proportional to the numberpresent. (a) If it is…

A: (a) Consider y as the number of bacteria at time t and the rate of change of bacteria can be written…

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

A: Consider the provided information, We assume that rate of change of amount of substance is…

Q: A chemical factory tank stores an amount of liquid. After it has started to drain, it has a given…

A: Solution

Q: In a city with 500,000 population, the rate of the spread of a new flu epidemic is proportional to…

A:

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

A: The general solution of a differential equation always contains a constant of integration. The…

Q: In a chemical reaction a substance decomposes at a rate proportional to the amount of substance…

A:

Q: In a certain bacteria culture the rate of increase in a number of bacteria is proportional to the…

A: Follow the steps below to solve a differential equation(in terms of x and y) by the variable…

Q: A man rows up a stream 4 ½ hours and finds that it requires only 2 ½ hours down the stream. If he…

A: To find: The rate of current. Given: A person rows up a stream 412 hours and 212 hours to down the…

Q: A man on a wharf is pulling a rope tied to a raft at a rate of 0.6 m/s. If the hands of the man…

A:

Q: A bacteria culture starts with 960 bacteria and grows at a rate proportional to its size. After 4…

A: The exponential growth formula is given by: P(t)=P0 ekt...(1) where P0 is initial population, k is a…

Q: Two cars are headed for the intersection of the two roads. If Car A is travelling south at 41 km/h…

A: Given problem is : Two cars are headed for the intersection of the two roads. If Car A is travelling…

Q: In a water bottling process, one-liter bottles are filled through a system that provides filtered…

A:

Q: The population of a district in a town is known to increase at a rate proportional to the number of…

A: We will find out the required initial population of the state .

Q: Given that bugs grow at a rate of 0.95 with a volume of 0.002. How many weeks would it take to fill…

A: Solution : given, Rate of bugs growing = 0.95 bug/second volume of a bug =0.002 unit I) number of…

Q: A certain population of bacteria is known to grow at a rate proportional to the amount present in a…

A:

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

A: Given: The population of a certain state is known to grow at a rate proportional to the numberof…

Q: A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start…

A: How far did the adults go? How long did that take?

Q: A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are…

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Q: If a IV fluid bag is Flowing out of a 1.0 liter bag at the rate of 0.4 cc/min how long will it take…

A: Total volume of fluid flowing out =1.0 litre rate of flowing =0.4 cc/min

Q: The legs of an elephant are much thicker in proportion to its body than the legs of a mouse. This is…

A:

Q: A bacteria culture starts with a population of 1000 bacteria, and after 2 hours, the population grew…

A: Solution and Explanation is given below

Q: A certain population of bacteria is known to grow at a rate proportional to the amount present in a…

A: Solve for bacteria after 20 hrs

Q: A 500-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 2 Ib…

A: Given:   Equation data is given

Q: A slightly different breed of Hippogriffs, living in the Rathlin Island—the northernmost point in…

A:

Q: A drug used to relieve anxiety and nervousness has a​ half-life of 13 hours. If a doctor prescribes…

A: Given that:                        Half life of drug = 13 hrsOne 2.2 mg tablet every 21 hr

Q: The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of…

A:

Q: In a certain bacteria culture the rate of increase in a number of bacteria proportional to the…

A:

Q: vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter…

A: Solution of the problem as follows

Q: Sugar dissolves in water at a rate proportional to the amount still undissolved. If there were 70 kg…

A: The amount of sugar present initially is 70 kg and at the end of 4 hours only 30 kg is left. The…

Q: In a certain rectangle, the length of one side is always two inches more than four times the length…

A: Given query is to find the rate of change area.

Q: The population of a bacteria increases at a rate proportional to the present number of bacteria ‘P0’…

A: Given problem is : The population of a bacteria increases at a rate proportional to the present…

Q: In a chemical reaction, a certain compound changes into another compound at a rate proportional to…

A: Let y be the unconverted amount of substance A at time t. Thus, the given information can be written…

Q: A certain type of bacteria is known to grow at the rate proportional to the amount that is present.…

A:

Q: A 25-liter gas cylinder contains 80% oxygen and 20%   helium. If helium is added at a rate of 0.2…

A: The volume of cylinder =25 litre The percentage of oxygen in the cylinder initially=80% The amount…

Q: The number of germs in a certain culture increases at a rate proportional to the number present. If…

A:

Q: If you have a tree that is 2.5 feet tall and it grows at a rate of 1.2, what equation would five you…

A: Equation that we use y= a * bx

Q: A puppy weighs 2.0 lb at birth and 3.5 lb 2 months later. If the weight of the puppy during its…

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.