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: For a certain square, the side is increasing at the rate of 2 mm/s. At what rate is the perimeter of…

A: We know       Perimeter (P) = 4 × ( side of square)

Q: A hose fills 2/8 of a pool in 3/6 of an hour. At this rate, how much of the pool will these hose…

A: given that  A hose fills 2/8 of a pool in 3/6 of an hour. Clearly 1/4 of a pool filled in 1/2 hour…

Q: a city grows at a rate directly proportional to its population. The initial pop. is 30 and it…

A: The rate of change of the variable (Population here) is proportion to the variable itself. Hence,…

Q: The half-life of the drug Morphine in the blood is 120 minutes. If 75 mL are given to a patient at…

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Q: A safety inspector determines that contamination from an abandoned factory site is spreading through…

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Q: I have 3/4 of a liter of juice to share with friends.  Together, they drank 2/3 of the juice.  How…

A: Total amount of juice =34 ltrAmount of juice they drank=23 of total amount of juice

Q: The population of bacterla In a culture grows at a rate proportional to the number of bacterla…

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Q: The half-life of Cesium-137 is 30 days. How much of a 200 mg sample would be left after 165 days?

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Q: Ahmed can run 4.3 m/s and Khaled can run 6.7 m/s. Ahmed is given a head start of 24 meters since he…

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Q: If human toenail grows at an average rate of about 0.13 inch a month.   1 year has 12 months. 1…

A: Given, Growth of human to nail =0.13 inch/month 1 year has 12 months. 1 inch is equal to 2.54 cm.…

Q: How many times more energy does a 450-nm blue photon have than a 656-nm red photon?  answer to three…

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Q: A box is partially filled with liquid. The length of the box is 11 inches. The width of the box is…

A: We have to find rate of change of height of liquid .Information is given below.

Q: At what rate is a car traveling if it goes 157.5 miles in 2.5 hours?

A: Given ,Distance travelled by car, d=157.5 milesTime taken, t=2.5 hours

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

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

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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.