A population numbers 17,000 organisms initially and grows by 14.6% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P=a⋅b^t where P=?

Q: The count of bacteria in a culture was 600 after 20 minutes and 2000 after 35 minutes.

A: 20,600 and 35,2000 Let the exponential model be y=abx. Substitute the given point to obtain the…

Q: The half-life of a substance is 1200 years. If the initial amount of the substance is 300 grams,…

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Q: The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2…

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Q: The count in a bacteria culture was 500 after 20 minutes and 1500 after 30 minutes. Assuming the…

A: Given that, the count in a bacteria culture was 500 after 20 minutes and 1500 after 30 minutes.…

Q: The count in a bacteria culture was 600 after 20 minutes and 1700 after 40 minutes. Assuming the…

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Q: The count in a bacteria culture was 400 after 10 minutes and 1200 after 35 minutes. Assuming the…

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Q: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.  Use…

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Q: The number of bacterla in a certain population is predicted to increase according to a continuous…

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Q: The count in a bacteria culture was 400 after 10 minutes and 1700 after 30 minutes. Assuming the…

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Q: A bird species in danger of extinction has a population that is decreasing exponentially A = A0ekt.…

A: Given A=A0ekt Initial population = 1400 when t = 0 after 5 years population is 1000

Q: The size of a threatened population of bottlenosed dolphins is decaying exponentially with a…

A: topic - exponential function

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 tumor is injected with 0.9 g of iodine -125, which has a decay rate of 1.5% per day. Write an…

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Q: A culture of bacteria obeys the law of natural exponential growth. If 140,000 bacteria are present…

A: We can make it easier for you.

Q: After 245 years half of a sample of radioactive element remains. Write the equation for modeling its…

A: First form the differential equation than solve it.

Q: A population of bacteria grows exponentially and their population doubles every 4.5 hours. If the…

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Q: Consider a population that begins growing exponentially at a base rate of 8​% per year and then…

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Q: The count in a bacteria culture was 400 after 10 minutes and 1300 after 30 minutes. Assuming the…

A: The values is:-

Q: The count in a bacteria culture was 300 after 20 minutes and 1600 after 30 minutes. Assuming the…

A: To begin with this question, we need to know the exponential growth formula that is Nt = N0ekt where…

Q: A doctor prescribes 225 milligrams of a therapeutic drug that decays by about 10% each hour. Write…

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Q: The count in a bacteria culture was 900 after 10 minutes and 1500 after 40 minutes. Assuming the…

A: NOTE: Refresh your page if you can't see any equations. . let the exponential function is in the…

Q: A population starts with 2,500 individuals and doubles every 40 years. Give an exponential model for…

A: The initial population is 2500. It gets doubled every 40 years. So after 40 years the population…

Q: In 2000, the population of Israel was approximately 6.04 million and by 2050 it is projected to grow…

A: The explicit form of the exponential growth model is defined as At=A0ekt. Where, A(t) denotes the…

Q: A cell population grows exponentially beginning with one cell. Which takes longer: increasing from…

A: Definition of the exponential functions helps to find the answer to the problem. A function is said…

Q: The size of a threatened population of bottlenosed dolphins is decaying exponentially with a…

A: To find out the population after 9 months.

Q: The count in a bacteria culture was 100 after 10 minutes and 1900 after 35 minutes. Assuming the…

A: Given data is : The count in a bacteria culture was 100 after 10 minutes and 1900 after 35 minutes…

Q: A scientist studying the Earth’s population growth over the last 20 years found that there was 5.96…

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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: The count  in a bacteria culture was 200  after 15 minutes and 1600 40 minutes assuming the count…

A: So we can model the growth of bacteria with an exponential function given by,             f(t)…

Q: The count in a bacteria culture was 500 after 15 minutes and 1900 after 35 minutes. Assuming the…

A: Given that, count of bacteria culture after 15 minutes = 500 count of bacteria culture after 35…

Q: The count in a bacteria culture was 700 after 20 minutes and 1200 after 35 minutes. Assuming the…

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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: The count in a bacteria culture was 400 after 10 minutes and 1700 after 35 minutes. Assuming the…

A: Given: The count in bacteria culture was 400 after 10 minutes and  1700 after 35 minutes.Assuming…

Q: A bird species in danger of extinction has a population that is decreasing exponentially (A =…

A: Given population equation - A = A0ekt                ................(1)A0 = Initial Population =…

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: An element with a mass of 120 grams decays by 27.5% per minute. What is the exponential equation…

A: Let us suppose that the initial mass of the element is M0 Let the mass after time t minutes be Mt…

Q: The count in a bacteria culture was 300 after 15 minutes and 1800 after 30 minutes. Assuming the…

A: It is given that, Initially, at time t1=15 min. the bacteria count was N1=300 While, at time t2=30…

Q: A material has an initial of 15 units. Which equation models the amount of the material y, decaying…

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Q: A population numbers 11,000 organisms initially and grows by 8.5% each year. Write an exponential…

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Q: The count in a bacteria culture was 500 after 15 minutes and 1100 after 40 minutes. Assuming the…

A: Let the exponential model is : y=a(bx)  Where x= time in minutes  y= number of bacterias

Q: If a village has a population of 2000 and a natural growth rate of 3.7% but has a carrying capacity…

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Q: The count in a bacteria culture was 300 after 15 minutes and 1500 after 30 minutes. Assuming the…

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Q: The count in a bacteria culture was 200 after 10 minutes and 1700 after 30 minutes. Assuming the…

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Q: When you moved into your dorm room, there were initially 40 termites. After 6 days, there were 125…

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Q: How is Calculus used to derive the exponential growth or decay model?

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Q: The population of Brgy. Sta. Isabel starts with 1,000 individuals and triples every 50 years. (a)…

A: Solution:-

Q: An endangered species of fish has a population that is decreasing exponentially. The population 5…

A: We will use concept of exponential growth.

Q: Joe scraped his knee after falling off his skateboard, leaving a wound with an area of 291 mm^2. The…

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Q: The count in a bacteria culture was 600 after 10 minutes and 1700 after 35 minutes. Assuming the…

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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.