The rate at which bacteria multiply is proportional to the instantaneous N numbers present. If the original number doubles in 2 hrs? When it will be tripled ?

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6 oz of this…

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Q: The bacteria in a culture can be assumed to multiply at a rate that at any given moment is…

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Q: Assume that the rate of evaporation for water is proportional to the amount of water in a bowl. If…

A: I am going to solve the given problem by using some simple calculus to get the required result.

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

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Q: Each side of a square is increasing at a rate of 2 cm/s. At what rate (in cm2/s) is the area of the…

A: we know square area, A = a2  , where a = side of square  To find the solution , we will…

Q: Suppose that the concentration of a bacteria sample is 60,000 bacteria per miliditer. f the…

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

A: Assuming continuous compounding P=P0eKt P→Population at moment in time P0→initial Population…

Q: There are currently 100 cells in a culture and it grows at a rate proportional to its size. After…

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Q: a)How quickly is the water leaving the barrel over the first two seconds? b)Will the water drain…

A: The solution is given below in the next step:

Q: Each side of a square is increasing at a rate of 6 cm/s. At what is the area of the square…

A: Given that, Area of square is  25cm2    Area A = x2 Where x is the side length. The area of square…

Q: The rate at which radioactive nuclei decay is proportional to the number of nuclei that are present…

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Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Simple rate of decay of radium problem....

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

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Q: The population of a certain municipality increases at the rate proportional to the present…

A: Here we solve the given population growth problem.

Q: The population of a city doubles in 50 years. How many years will it be four times as much? Assume…

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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: 4. In a culture of yeast, the amount of active ferment grows at a rate proportional to the amount…

A: Let's work on the problem straight from the statement "the amount doubles in 1 hour": let the…

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 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 3 cm/s and its width is increasing at a rate of…

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Q: Each side of a square is increasing at a rate of 7 cm/s. At what rate (in cm2/s) is the area of the…

A: We have to find rate of change of area

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: Two cars start moving fr km/hr. At what rate is the

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

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

A: In a certain culture of bacteria, the rate of increase is proportional to the number present. We…

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: Consider the given situation, Let the length of the rectangle be ‘l’ and breadth be ‘b’.Area of…

Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate (in cm2/s) is the area of the…

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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 14-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

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Q: A wet towel hung from a clothesline to dry loses moisture through evap-oration at a rate…

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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: Length of rectangle, x= 7 cm, Width of rectangle, y= 4 cm, Rate by which length is increasing is…

Q: A mold grows at a rate proportional to its present size. If the original amount doubles in one day,…

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Q: The growth rate of a bacteria culture is proportional to the number of bacteria present. If a…

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

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Q: A cup of coffee cools at rate proportional to the difference between the constant room temperature…

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

A: Given that, the number of germs in a certain culture increases at a rate proportional to the number…

Q: The rate at which yeast cells multiply is proportional to the number present. If the original number…

A: Given, The rate at which yeast cells multiply is proportional to the number present. the original…

Q: In 10 minutes, the body cools from 75 to 55 degree Celsius when temperature of the surrounding is 31…

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Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We can find the answer as below.

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

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Q: Given 100 grams of bacteria that decreases at a rate of 1/2 per year. What would be an appropriate…

A: Initial value: 100, Rate: 1/2 per year(decreases). So, the population equation is p(t)=100e-12t…

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

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Q: If the diameter of a piece of candy was initially 26 mm and after 30 minutes it measured 5mm, what…

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Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

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Q: A culture of bacteria grows at a rate that is proportional to the present number. It is found that…

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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 have to find

Q: 1. After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is…

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Q: 2. The population of a country doubles in 50 years. How many years will be 5 times as much? Assume…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.