Write the exponential function y=25e^0.098t in the form y=ab^t. Find b accurate to four decimal places. If t is measured in years, give the percent annual growth or decay rate and the continuous percent growth or decay rate per year

Q: The radioactive isotope of lead Pb-209, decays at a rate proportional to the amount present at any…

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

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: What is the total amount of 4500 TL with 3,7 % continuously compound interest after 3 years?

A: Given Present value (P)= 4500 TL Rate (r)=3.7% Number of years (t)= 3

Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

Q: odine -131 has a half-life of approximately 8 days. ind the amount of iodine-131 left from a 100…

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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: The rate of a continuous money flow starts at $1000 and increases exponentially at 5% per year for 4…

A: We use the formula                                P = ∫0T f(t)e-rt dt

Q: A doctor prescribes 150 milligrams of a therapeutic drug that decays exponentially. If the half-life…

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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: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into…

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Q: The count in a bacteria culture was 100 after grows exponentially, What was the initial size of the…

A: Consider the function with exponential growth and the given conditions. a=aoektwhere, ao=initial…

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: 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: The accumulated amount of P8000 is P10000 after 2 years, calculate the interest rate if it is…

A: The accumulated amount of $8000 is $10000 after 2 years,   We have to calculate the interest rate…

Q: After 2250 years, 25% of a radioactive material remains. If the rate of decay of the material is…

A: Half-life = 0.693/Decay constant(lambda)

Q: sample of a radioactive isotope had an initial mass of 390 mg in the year 2007 and decays…

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Q: Emma invested $630$630 in an account in the year 1997, and the value has been growing exponentially…

A: for growing exponentially

Q: Ava invested $470$470 in an account in the year 2000, and the value has been growing exponentially…

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Q: The count in a bacteria culture was 200 after 15 minutes and 1600 after 30 minutes. Assuming the…

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Q: The count in a bacteria culture was 800 after 10 minutes and 1200 after 35 minutes. Assuming th…

A: Please refer to the image below

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 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: 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: The U.S. Census Bureau keeps a running clock totaling the U.S. population. On September 20, 2012,…

A: Consider t be the time in years after the September 20, 2012 at 8.11 p.m. EST and y(t) be the…

Q: Among various populations of plants or animals, diseases spread exponentially. Use the function…

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Q: A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. How do…

A: Consider the given information ,tumor is injected with 0.9gm

Q: the amount of drug in a person’s bloodstream can be modeled by an exponential decay function.…

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Q: The population of Glenbrook is 375,000and is increasing at the rate of 2.25% per year. Predict when…

A: To find: When the population is 1 million. Given: Initial population is 375000 and rate of…

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

A: Given information:  Cockroach population decrease by 18% in 12 years.…

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: Three thousand dollars is deposited in the bank at 4% interest compounded continuously. What will be…

A: It is given that Money in the account $3000 Interest rate   We have to find the average value of…

Q: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

A: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

Q: proportional to A, weight W, and height H. A and W measurement values taken from different people…

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Q: An accidental spill of 65 grams of radioactive material in a local stream has led to the presence of…

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Q: A biologist has 6827 gram sample of a radioactive substance. Find the mass of the sample after four…

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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: A quantity with an initial value of 510 grows exponentially at a rate such that the quantity doubles…

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Q: An unknown radioactive element decays into non-radioactive substances.  In 660 days the…

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Q: A bacteria culture starts with 100 bacteria and grows exponentially, after 1 hour the population is…

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Q: An unknown radioactive element decays into non-radioactive substances. In 880 days, the…

A: The half life of a radioactive element is the time it takes to decay half of its original isotope.…

Q: The count in a bacteria culture was 600 after 20 minutes and 1500 after 35 minutes. Assuming the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The count in a bacteria culture was 400 after 20 minutes and 1000 after 40 minutes. Assuming the…

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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: A sample of bacteria taken from a river has an initial concentrationof 2.5million bacteria per…

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Q: Find the accumulated amount after 5 years if $4500 is invested at 4%/year compounded continuously.

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Q: A quantity with an initial value of 390 decays exponentially at a rate of 8.5% every 9 weeks. What…

A: We give the change of the quantity as a function of time as y(t)=390 e-0.0859t where t is in weeks.

Q: The count in a bacteria culture was 800 after 10 minutes and 1800 after 35 minutes. Assuming the…

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Q: A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…

A: Given:A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…