Q1) The doubling time for a certain virus is 3 yr. How long will it take for the virus to increase to 10 times its current population level?

Q: 9) Suppose a culture of bacteria starts with 60 bacteria and grows to 500 bacteria in 6 hours. Find…

A: ,

Q: 3. A small metal bar, whose initial temperature was 20° C, is dropped into a large container of…

A: Let's find.

Q: Suppose a metal ball is heated in an oven at 195 °C for a very long time. After, it was removed and…

A: Let the temperature of metal ball at time t be:  y(t) Surrounding temperature is:  A = 25°C…

Q: (2) Researchers have determined that Titan (one of the Moon's of Saturn) has liquid water. If we…

A: The average distance between Earth and Titan is 890.74 Million miles which is about 1433.5 Million…

Q: In order to ensure compliance with the law, Miguel routinely overshoots the weight of his tortillas…

A:

Q: A rubber ball bounces to 3/4 of its initial height when dropped on a hard surface. what is the…

A: Given: The ball is dropped from the height 10 meters. The ball bounces 34 of its initial height.…

Q: A plant grows 1.67 cm in its first week. Each week it grows by 2% more than it did the week before.…

A: Just observe that increment of 2% to the original 100% means 102% which is equal to 1.02

Q: A candy company wants to produce 25 kilograms of a special 35% fat content chocolate to conform with…

A: Given: A candy company wants to produce 25 kilograms of a special 35% fat content chocolate.To…

Q: 2) Water is pouring into an inverted cone at the rate of 8 cubic me- ters per minute. If the height…

A: Given that Height of cone h=12 m radius of its base r=6 m rate of pouring water into cone dVdt=8 m3

Q: A device has a constant failure rate of A= 10-5 failures per hour. (a) What is its reliability for…

A: Failure rate is the frequency with which an engineered system or component fails, expressed in…

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: Given: The amount of water at 3:56 PM is 10452 L and amount of water at 4:12 PM on same day  is 8092…

Q: An airplane, flying horizontally at an altitude of 1km, passes directly over an observer. If the…

A: Given: y = altitude = 1km  constant speed of plane dx/dt = 240kph

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Given :Half life of Palladium-100= 4 days

Q: 9. The mass of a radioactive substance is 400mg and decreases by 6% per year. What is its mass after…

A: The mass of the radioactive substance is 400mg and decreases by 6% per year.

Q: Suppose you are a pharmacist and a customer asks you thefollowing question. His child is to receive…

A: Given: Total nausea medicine received by child=13.5 mlTotal time period=54 hours To Find: The amount…

Q: A ball is thrown upward from the ground with an initial speed of 25m/s. at the same instant, another…

A: Solution   Given a ball is thrown upward from the ground with an initial Same from Speed of 25m/s,…

Q: A Computer on the 4 Mbps network is regulated by a token bucket. The bucker is filled at a rate of…

A: Let T be the time taken by computer to transmit full 6Mbps Let c = initial capacity =8Mb r =filling…

Q: Solve using Euler’s Method. Approximate up to 5 decimal places.

A:

Q: Element X is a radioactive isotope such that every 4 years, its mass decreases by half. Given that…

A:

Q: (b) Use the model from part a to determine number of bacteria, rounded to a whole nun after 2 hours:

A: we have to find

Q: 400 inch-lbs of work is required to stretch a spring from its rest length to 10 inches beyond its…

A: Given:- 400 inch-lbs of work is required to stretch a spring from its rest length to 10 inches…

Q: A runner starts at the beginning of a runners' path and runs at a constant rate of 5 mi/hr. Fifteen…

A: First, we need to calculate the relative speed which is, the difference between the speed of the…

Q: A hypothetical square grows so that the length of its diagonals are increasing at a rate of 8…

A:

Q: The sum of the reciprocal s of Rehman's ages (in years) 3 years ago and 5 years from now is -. 1…

A: Age Related Problem

Q: If the tank is completely full, how much is overflowing if 530 GPM is being taken off the bott

A: Given: Let the rate of filling be Qin = 1250 GPM  the rate of draining be Qdrain = 530 GPM Because…

Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

A: we have to determine time before the region is again habitable

Q: If a patient has an order of 400 mg IV q8h and the drug has a half life of 8 hours, what is the…

A: The half-life decay is given by the formula,

Q: A certain bacteria population is known to quadruples every 90 minutes. Suppose that there are…

A:

Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km2, and water flows…

A:

Q: The population of one state increases at a rate numerically equal to the cube root of the…

A:

Q: 15. A ball drops from a height of 120 dm. If each time it strikes the ground it bounces 3/4 of the…

A:

Q: A rubber ball is made to fall from a height of 70 feet and is observed to rebound 3/4 of the…

A: The sum, S, of the infinite geometric series, a+ar+ar2+ar3+⋯ is defined as S=a1-r. Here a is the…

Q: If paper napkin 0.10 inch thick could be folded so that it was half as large but twice as thick,…

A: paper napkin 0.10 inch thick could be folded so that it was half as large but twice as thick,…

Q: how long will it take $800 to triple if it is invested at an annual intrest rate of 5.3%

A: P=$800 , R=5.3%

Q: In a factory there are 100 skilled, 250 semi-skilled and 150 unskilled workers. It has been observed…

A:

Q: Suppose that a bacteria population doubles every eleven hours.  If the initial population is 2,000…

A:

Q: 1. Suppose a culture of 300 bacteria at BIO Farm is put into Petri dish and the culture doubles…

A:

Q: As dry air moves upward, it expands and, in so doing, cools at a rate of about 1o C for each…

A:

Q: Exercise 2 The volume of a cube is increasing at the rate of 1200cm3/min at the instant its edges…

A: We have to find at what instant edges changing.

Q: Find the dimensions of the largest rectangle that can be inscribed in an isosceles triangle if one…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 10. The mass of a radioactive substance is 1000mg and decreases by 7% per year. What is its mass…

A:

Q: How long will it take a population of bacteria to reach a certain size, given that we know its…

A: How long will it take a population of bacteria to reach a certain size, given that we know its…

Q: The population of certain species of bats doubles every five hours, initially there are 40 Båts (a)…

A: General formula for exponential growth is given by P(t)=P0ert. Since initially there are 40 bats…

Q: . Use the variation of parameters formula together with the exponential from part 3) to find the…

A: As per the question we have the following second order linear non-homogeneous differential equation…

Q: 4. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard's average…

A: Given: a) A lizard accelerates from 2 m/s to 10m/s in 4 seconds. What is lizards average…

Q: Device 2 is capable of detecting seismic changes up to a distance of 1.4 times that of device 1.…

A: In this we have to do the given instructions and approximate the value to the nearest 100,000 and…

Q: 4. If caffeine has a half-life of 2 hrs., how many of 140 mg of caffeine remain in Mr. Moreno's…

A:

Q: 1. A tank is shaped like an upside-down pyramid, with a base of 4 meters and a height of 12 meters.…

A:

Q: The original quantity of a radioisotope was 100 mCi. How long will take to reduce to 75 mCi, if the…

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.