A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 hours there are 10,000 bacteria. At the end of 5 hours there are 40,000. How many bacteria were present initially?

Q: 74 rabbits are released in an isolated area free of predators. After 2 years, it is estimated that…

A: Given, After 2 years, population of rabbit increased to 296 (74*4) , which is four times of initial…

Q: bacillus subtilis, a type of a bacteria responsible for the decomposition of organic matter, grows…

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Q: The population of a certain community follows the law of exponential change. If the present…

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Q: Find the equation of an exponential function of the form f(x) = a · bª that passes through the…

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Q: A radioactive substance decays exponentially. A scientist begins with 130 milligrams of a…

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Q: You go to the doctor and he gives you 16 milligrams of radioactive dye which decays exponentially.…

A: for the given amounts and time of radio active dye  time we remain at doctor's office is calculated…

Q: Find a formula for the exponential function passing through the points (-1, 4/3) and (3, 108).

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Q: The population of Aarb and the population of Bullm are each growing exponentially. In the year 2000,…

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Q: Find a formula for the exponential function passing through the points (-1,2) and (1,8) y =

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Q: -a) A population of bacteria grows exponentially cond their population doubles every 4.s hours. If…

A: The time taken by the bacteria to double its population is 4.5 hours. The initial population of the…

Q: A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a…

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Q: f the population of a certain county was 100,000 in 1998 and 110,585 in 2008, and if the population…

A: Given: The population of a certain county was 100,000 in 1998 and 110,585 in 2008.   Formula used:…

Q: Beginning on January 1, 2000, the populations of wolves and rabbits in a certain forest both grew at…

A: According to question,Given dataInitial population of wolves = 65,Rate of increasing Wolves by 25%…

Q: Find a formula for the exponential function V=h(t) that gives the value of an item initially worth…

A: Find a formula for the function exponential function v=ht that gives the value of item initially…

Q: A radioactive substance decays exponentially. A scientist begins with 200 milligrams of a…

A: Formula: N(t)=N0exp-0.693tt1/2whereN0=initial amount of substancet1/2=half life of…

Q: A radioactive substance decays exponentially. A scientist begins with 130 milligrams of a…

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Q: For a certain patient, a dose of Acetaminophen decays exponentially in their blood stream with a…

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Q: The number of bats in a colony is grown exponentially. After two years there are 180 bats. After…

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Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population…

A: The exponential growth model is A = Pek·t where A is the number of bacteria after time t hours, P is…

Q: A dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of the anaesthetic…

A: We can use exponential decay function to solve the problem

Q: Find a formula for the exponential function passing through the points (-1, 1/2) and (2, 32).y =

A: Let the function is y=a(bx) Given, it passes through (-1, 1/2) and (2, 32).

Q: Suppose a population of insects increases according to the law of exponential growth. There were 130…

A: Given- There were 130 insects after the third day of the experiment and 380 insects after the…

Q: A colony of fruit flies is growing according to the exponential law P(t) = P0ekt, and the size of…

A: Given: P(t)=P0ektwhen t=9, then P(t)P0=2

Q: Find a formula for the exponential function passing through 4 the points (-1,) and (3,108) y =

A: Exponential function: - An exponential function in mathematics is one of the form f(x)=abx, where…

Q: The count in a bacteria culture was 400 after 15 minutes and 1400 after 35 minutes. Assuming the…

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Q: The initial size of a bacteria culture that grows exponentially was 10,000. After 1 day, there are…

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Q: It is known that a certain kind of algae in the Dead Sea can double in population every 3 days.…

A: Given:  The population doubles every 3 days.  Initial population = 2,000,000 To find:  a) How long…

Q: 9. The number of bacteria in a Petri dish grows exponentially, starting with just 1 bacterium, but…

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Q: The count in a bateria culture was 500 after 15 minutes and 1100 after 30 minutes. Assuming the…

A: Aim:  To find the expression for the bacteria count N(t) as a function of time 't' (in minutes).…

Q: Find a formula for the exponential function passing through the points (-3,5/27) and (3,135)

A: The objective is to find the exponential function

Q: Bacteria in a certain culture increases at an exponential rate. If the number of bacteria triples in…

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Q: through

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Q: You go to the doctor and he gives you 14 milligrams of radioactive dye which decays exponentially.…

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Q: A lab culture initially contains 500 bacteria. Two hours later, the number of bacteria decreases to…

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Q: count in a bacteria culture was 700 after 15 minutes and 1000 after 35 minutes. Assuming the count…

A: We need the exponential growth formula :                                 N(t) = N0 ekt ,…

Q: A radioactive substance decays exponentially. A scientist begins with 170 milligrams of a…

A: Given that a radioactive substance decays exponentially. A scientist begins with 170 miligrams of a…

Q: Some populations, such as bacteria, can be expected under the right conditions to show exponential…

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Q: You go to the doctor and he gives you 13 milligrams of radioactive dye which decays exponentially.…

A: Exponential model is given by y=y0ekt, where y0  is the initial amount of the element, k is the…

Q: Find the formula for an exponential function that passes through the two given points. (0,1000) and…

A: Suppose that the function is of the form

Q: Find formula for the exponential function passing through points (-1,3/4) and (2,48)

A: Given: The given points are, x1,y1=-1,34x2,y2=2,48 The objective is to find the formula for the…

Q: An experiment compares two bacterial cultures, both growing exponentially. Culture A begins with…

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Q: Find a formula for the exponential function passing through the points (−2,250)and (1,2)

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Q: Find a formula for the exponential function passing through the points (-1,5) and (3,54) y =

A: use the general form of exponential function . and use this point to get the coefficient of…

Q: A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a…

A: The number of atoms N of a radioactive substance which remain undecayed after an elapse of time t…

Q: A radioactive substance decays exponentially. A scientist begins with 180 milligrams of a…

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Q: Find a formula for the exponential function passing through the points (-2,2/9) and (1,6)

A: Find a formula for the exponential function passing through the points -2,29 and 1,6. Let y=abx be…

Q: In 2010 , the population of a colony is 12000  , and is decreasing exponentially at a rate of 2.1%…

A: (a) It is given that, in 2010 the population of a colony is 12000, that is, the initial amount is P…

Q: It is known that a certain kind of algae in the Dead Sea can double in population every 5 days.…

A:

Q: A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a…

A: It is an important part of statistics. It is widely used.

Q: It is known that a certain kind of algae in the Dead Sea can double in population every 3 days.…

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.