When you moved into your dorm room, there were initially 40 termites. After 6 days, there were 125 termites. To predict the future population of your termite infestation, create a exponential growth model of the form y=Ca^x where x represents days.

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

A: The exponential growth model is defined as, y = a(1 + r)t, where a is the initial amount, r is the…

Q: Suppose a study is completed that finds that the number of cockroaches in Chandler decreases by 18%…

A: Given: Initial population of cockroaches = 3.5 millions = 3500000  Rate of decrease = r=18%=0.18…

Q: If a total number of infections of a viral disease was observed to be 48 in day 27 and 900 in day…

A: Since the growth is exponential , so it is of the form P(t)=P0ert where P(t) is the number of…

Q: Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the…

A: Given data: Diseases tend to spread according to the exponential growth model. The growth rate =…

Q: A student is 25 years old and the world has a population of 6.2 billion. Assuming that the…

A: Given,  Student's current age = 25 Student's future age = 68 Time (t) = 68 - 25  = 43 Annual growth…

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: A stock portfolio increased in value from $100,000 to $117,000 in 2 years. What rate of interest,…

A: To find: The rate of interest, compound continuously. Given: The stock portfolio increased from…

Q: If the starting point is 30, and the growth rate is 15%, choose the exponential function.

A: To find the exponential function with the given data

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 population of the world in 1987 was 5 billion and the relative 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: In 2011 a country had a population of 117 million and a growth rate of -0.372%.  Assuming that this…

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Q: The count in a bateria culture was 800 after 15 minutes and 2000 after 30 minutes. Assuming the…

A: Let I be the initial size of culture,  the exponential growth formula is given by

Q: If a certain substance exponentially decays from 100 grams to 20 grams in 3 years. How much of the…

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Q: The count in a bacteria culture was 500 after 15 minutes and 1900 after 40 minutes. Assuming the…

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Q: A quantity with an initial value of 5700 decays exponentially at a rate of 7.5% every 2 days. What…

A: Given data: The given rate is r=7.5%. The given time is t=2 days. The initial value is A=5700. The…

Q: The count in a bacteria culture was 500 after 20 minutes and 1700 after 30 minutes. Assuming the…

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Q: The count in a bacteria culture was 400 after 10 minutes and 1100 after 35 minutes. Assuming the…

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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 student is 19 years old and the world has a population of 6.6 billion. Assuming that the…

A: Given Present population (P) = 6.6 Rate (R) = 0.6% Time  (n) = 72-19= 53

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: 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: 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 700 after 15 minutes and 1300 after 30 minutes. Assuming the…

A:

Q: suppose a study is completed that finds that the number of cockroaches in chandler decreases by 18%…

A: Given: Initial population of cockroaches = 3.5 millions = 3500000  Rate of decrease = r=18%=0.18…

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: Because of an economic slump, a company finds that its annual profits have dropped from 700 thousand…

A: First we shall find profit function with setting intial time 2006

Q: Suppose a new mosquito-borne virus has emerged and has caused 550 cases to- date. The number of…

A: A = A0(e-kt)  Where , k = Rate , t = time

Q: In 2011, the population of a district was 31,600. With a continuous annual growth rate of…

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Q: The news of the resignation of a public official is broadcast frequently by internet news media and…

A: Exponential model of growth or decay is given as: P=P0ert, where P0 is initial population, r is rate…

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…

A:

Q: The count in a bacteria culture was 700 after 20 minutes and 1400 after 30 minutes. Assuming the…

A: Given data: Count in bacteria culture after 20 mins=700 Count in bacteria culture after 30…

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 global recession caused a restaurant chain’s annual profits to fall. In 2018, the annual return is…

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

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: If 100 grams of a radioactive material diminish to 80 grams in 2 years, find the half-life of the…

A: Let the given condition can be modeled as  y=y0eλt   where, y=  Final quantity y0= Initial quantity…

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: Sales of portable MP3 players grew approximately exponentially from ​$0.05 billion in 1999 to ​$0.60…

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Q: Suppose that a population that is growing exponentially increases from 800,000 people in 2010 to…

A: the exponential model is of the form, At=A0ekt where A0 original amount of the entity, t is the…

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

A: Solution:-

Q: The median household income (adjusted for inflation) in Seattle grew from $42,500 in 1990 to $75,200…

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Q: If an account with initial amount of 2000 dollars earns 10% interest compounded continuously, how…

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Q: A biologist is monitoring the population of a rare species of Jackelope. The initial population size…

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Q: There were ( 376 ) people affected by corona pandemic in a region on 1 January , 2021. How long it…

A: Using differential equations we can model up a formula for exponential growth rate. Here we use such…

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.