In a chemical reaction, a certain compound changes into another compound at a rate proportional to the unchanged amount. There is 40 grams of the original compound initially and 35 grams after 1 hour. When will 75 percent of the compound be changed?

Q: The number of bacteria in a bowl increases at a rate of 20.8% per hour. There are currently 12…

A:

Q: A helium balloon looses 10 % of its volume every 6 hours. What percentage of the original volume…

A: .Volume looses in 6 hours= 10% of V= 0.1V Volume losses in 1 hour=  0.1V6 Volume losses in 27 hours=…

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: if the full capacity of a tank is 20 liters, and the tank is only filled with 16 liters, then what…

A: Capacity is the measure of the volume that can be occupied in a container.

Q: A man weighing 600 kg has been losing 3.12% of his weight each month with some heavy exercises and…

A: To determine the weight of man after 20 months.

Q: A particular type of bacteria grows at a rate of 59 % per day. If my dog got infected with 9000…

A: It is given that p=9,000, r=0.59 and t=14.

Q: A bacteria culture starts with 300 bacteria and grows at a rate proportional to its size. After 5…

A: " Since you have posted a question with multiple subpart, we will solve first three subpart for you.…

Q: The amount of caffeine in the bloodstream decreases by 24% every hour. A can of Rock Star energy…

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Q: When water is released from the Kinzua Dam it is released gradually. The water level in Kinzua…

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Q: The growth rate of a colony of rabbits is 40% per month. If the initial population of the colony 100…

A: The initial population of the rabbits is 100. It is given that the growth rate of rabbits is 40% per…

Q: The half-life of radioactive radium (226Ra) is 1599 years. What percent of a present amount of…

A:

Q: A population is growing at a rate proportional to its size. After 8 ​years, the population size was…

A: Let consider P(t) be the population at a time t. Let P0 is the initial population at time t = 0. To…

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.