A common inhabitant of human intestines is the bacterium Escherichia coli, namedafter the German pediatrician Theodor Escherich, who identified it in 1885. A cell ofthis bacterium in a nutrient-broth medium divides into two cells every 20 minutes.The initial population of a culture is 50 cells.(a) Find the 1elative growth rate.(b) Find an expression for the number of cells after t hours.(c) Find the number of cells after 6 hours.(d) Find the rate of growth after 6 hours.(c) When will the population reach a million cells?

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

A: Given: The population of a certain bacteria in a laboratory sample is 100 and it is doubles in…

Q: The rabbit population at the city park increases by 9% per year. If there are initially 289 rabbits…

A:

Q: suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per…

A: Population decay

Q: A bank pays interest at a rate of 5%. What is the yearly multiplier if interest is compounded (a)…

A:

Q: Ten thousand dollars is invested at 6.5% interest compounded continuously. When will the investment…

A: Given that, Ten thousand dollars is invested at 6.5% interest compounded continuously. We have a…

Q: Since the data obtained as a result of 5 observations of an experiment is ∑ log Xi = 6.27, what is…

A: n = 5 ∑ log Xi = 6.27 We have to find the geometric mean.

Q: The population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year.…

A: Given The population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year.…

Q: The mass of caffeine in the bloodstream decreased rapidly at first, and then more slowly.

A: Given statement: The mass of caffeine in the bloodstream decreased rapidly at first, and then more…

Q: In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear…

A:

Q: A bacteria population grows by 10% every 3 days. Based on this, if we initially have 2,000…

A: First of all we should know that the growth is exponential so formula will be: Nd = N0ekd where N0…

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

A:

Q: This year there were 3,000 new births in a county, but new births are expected to grow at a rate of…

A: This year there were 3,000 new births in a county, but new births are expected to grow at a rate of…

Q: Find a formula for the exponential function passing through the points (-2, - -) and (1,20) 16

A: -2,516 and 1,20 Let the exponential function be yn=abxn. Substitute both the point in the assumed…

Q: In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the population had…

A: Given,           In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the…

Q: Find a formula for the exponential function passing through the points (-2,-) and (1,10) y =

A: On solving this we will asume firstly general exponential function so  we will get

Q: How long would it take for a population to double if the population growth is 0.5%? please show your…

A:

Q: Find a formula for the exponential function passing through the points (-3, 2 / 27) and (1, 6). y =

A:

Q: 5:52. The number of bacteria in a certain culture was found to be 4 x 10° at noon of one day. At…

A:

Q: Scientists can determine the age of ancient objects by the method of radiocarbon dating. The…

A: Given query is to find the age of the parchment.

Q: A CERTAIN RADIOACTIVE MATERIAL IS KNOWN TO DECAY AT A RATE PROPORTIONAL TO THE AMOUNT PRESENT. IF…

A: Given that, after one hour, the 10% of the material is decayed. find the expression of the material…

Q: Suppose the population of certain fungi in a laboratory sample is 12. (A) If it quintuples in…

A:

Q: 2.A mold population is growth at 8% every three months. If there is initially 3 cubic centimeters of…

A: Formula : Population Growth: P=Po(1+r)n r= rate of growth Po =initial value P= present Value n= no…

Q: The population of Northern Cascadia is growing at a rate of 20% every 3 years. Assuming that it…

A: Topic: percentage

Q: he population of greater Lafayette is increasing at a rate of .95% each year. If the population was…

A:

Q: A population of cattle is increasing at a rate of 100 + 20t per year, where t is measured in years.…

A: Given : A population of cattle  is increasing at the rate of 100+20t per year

Q: A mold population is growth at 8% every three months. If there is initially 3 cm3 of mold, when will…

A: Formula for population growth is  P=P0ert where P = final population after time t P0 = initial…

Q: Suppose the amount of Carbon-14 remaining in a sample of 100 milligrams after X years can be…

A:

Q: A wooden artifact from an ancient tomb contains 20 percent of the carbon-14 that is present in…

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Q: A certain element decays at a rate of .000163/year. Of a piece of this element of 450 kg, how much…

A:

Q: The population of a city is 89​,000. If the population grows continuously by 3.2​% per​ year, in how…

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Q: A toxic radioactive substance in the amount of 7 miligrams per square centimeters is detected in the…

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Q: alf-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only…

A:

Q: Suppose that in a memory experiment the rate.of memorizing is given by M'(t) = - 0.0031? +0.4t where…

A: The solution is:

Q: Suppose Shunreca Garner invested $8000 in stocks and the investment grew exponentially to $10000 in…

A: To use the exponential model to 1) determine the  growth rate and 2) to calculate the value after 15…

Q: A species is considered to be endangered if it is expected to be extinct within 20 years. A…

A:

Q: Suppose that a population in a particular city is 46,581 in 2010. What is the population after 15…

A: The population growth is modelled using the equation: N(t)=N01+rt, where N0 is the initial…

Q: Find a formula for the exponential function passing through the points (-2,- -) and (1,20) 25

A:

Q: 6.05% interest compounded continuously?

A:

Q: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

A:

Q: In one experimental study, the growth of a certain insects is increasing at a rate proportional to…

A: Given: The growth of insects is increasing at a rate proportional to the number present. To Find:…

Q: The population of deer in Culberson County, Texas, is declining at an estimated rate of 0.8% per…

A:

Q: How much would you expect systolic blood pressure to change if a person commits to reducing their…

A: From the given information expect systolic blood pressure to change if a person commits to reducing…

Q: The population of certain species of bats doubles every five hours, initially there are 40 Båts (a)…

A: General formula for exponential growth is given by P(t)=P0ert. Since initially there are 40 bats…

Q: Imagine that COVID-19 had spread exponentially in Maine since the first case (on March 12). Using…

A:

Q: A new car that sells for $19,000 depreciates (decreases in value) 21% each year. What is the decay…

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Q: A tank with a capacity of 300 litres initially contains 150 liters of pure water. Brine contains 3gm…

A: Solve the question 1 Capacity of tank=300litres Amount of pure water in tank initially=150litres…

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

A:

Q: Find a formula for the exponential function passing through the points (-1,3232) and (1,6)   Y= ?

A:

Q: Suppose that in a memory experiment the rate of memorizing is given by M'(t)= -0.009t² +0.8t where…

A: Given

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.