The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours it is observed that 500 bacteria are present. After 10 hours 5000 bacteria are present. What was the initial number of bacteria?

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Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

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Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: Initially 35 grams of radioactive substance was present. After 5 hours the mass had decreased by 11…

A: Given:- Initially 35 grams of radioactive substance was present. After 5 hours the mass had…

Q: A tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

Q: A freshly brewed cup of coffee has temperature 95°C in a  20°C room. When its temperature is 70°C,…

A: Given that, Initial temperature of coffee is T0=95°C, surrounding temperature is Ts=20°C. Also,…

Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: It would be best to express length, width, and area as functions of time. I’ll set x = width, y =…

Q: A certain population of bacteria grows such that its rate of change is always proportional to the…

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Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

Q: at a rate proportional to the current population, and in the absence of other factors, the…

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A: Given the rate of change= 0.6+4/(t+2)2 feet per year To find the total number of feet grown during…

Q: A bacteria population starts with 400 bacteria and grows at a rate of r(t)= 450.268 e ^1.12567t per…

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Q: Initially 100 milligrams of a radioactive substance were present. After 6 hours the mass had…

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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: The rate at which bacteria multiply is proportional to the instantaneous N numbers present. If the…

A: Let y(t) represents the number of bacteria present in the culture after t hours. Let the initial…

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

A: We have to find the area of rectangle increasing

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

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Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: Given: The length of a rectangle is increasing at a rate of  9cm/s and its width is increasing at a…

Q: After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is present.…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Let us assume that the rate of change of the amount of material is proportional to the amount of…

Q: A yeast grows at a rate proportional to its present size. If the original amount doubles in two…

A: Let v(t) be size of yeast at t time Therefore, ds/dt  ∝ s(t) ds/dt  = ks   [k is proportionality…

Q: The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of…

A: We need to find reat of change of area.

Q: The height of a triangle is increasing at a rate of 4 cm/s while the area of the triangle is…

A: Let the height, base and area of a triangle be 'h', 'b' and 'A' Given, dhdt=4 cm/sdAdt=56 cm2/s

Q: The rate at which the body cools is proportional to the difference in temperature of the body and…

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Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

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Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

Q: An ice cube that is 3 cm on each side is melting at a rate of 2 cm3 per min. How fast is the length…

A: Given: Length of cube L=3cm Rate of melting =-2cm3

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

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Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

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Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

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Q: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

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Q: Assume that a snowball melts so that its volume decreases at a rate proportional to its surface…

A: Let V denote the volume and A denote surface area. Rate of melting is proportional to its surface…

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Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

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Q: After 2 days, 10g of radioactive chemical is present. Three days later, 5g is present. How much of…

A: Given:      After  2 days, 10g of radioactive chemical is present. Three days later5 g chemical is…

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

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Q: ladder away

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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 100 gallon tank is filled with brine containing 60 pounds of dissolved salt. Water runs into the…

A: Form the differential equation of first order and solve to get the answer.

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

A:

Q: The length of a rectangle is decreasing at the rate of 5 cm/s and its width is increasing at the…

A: Area of a rectangle = length× width Rate of change with respect to time is D/Dt

Q: he surface area of a cube is increasing at a rate of 122.2 cm2/s. At what rate is the side length of…

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Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

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Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 66°C, it…

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Q: Initially 47 grams of radioactive substance was present. After 10 hours the mass had decreased by…

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Q: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

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Q: An apple pie with an initial temperature of 170 -C is removed from the oven and left to cool in a…

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Q: A wet towel hung on a clothesline to dry outside loses moisture at a rate proportional to its…

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Q: Initially 25 grams of radioactive substance was present. After 10 hours the mass had decreased by…

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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.