1) For a period of time, an island's population grows at a rate proportional to its population. If the growth rate is 3.8% per year and the current population is 1543, what will the population be 5.2 years from now?

Q: If a population is recorded at 1,200 in the year 2000 and the rate of increase is a steady 50 people…

A: Given date  Initial population Po=1200 in the year 2000 (t=0) Rate of increase is a steady =50…

Q: 4. Radium decomposes at a rate proportional to the amount present. If half the original amount…

A: Solve differential equation

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

A:

Q: If the population of a small city is 45,000. If the population grows continuously by 5% per​ year,…

A: Here we use compound interest based formula. If p is present population, r is rate of growth of…

Q: 4. How much should be invested at 12.5% compounded continuously to end up with $1000 at the end of 5…

A:

Q: If the population of the earth was found to be 3.5 billion in 1970, and Is Increasing at a rate of…

A: The population of the earth was 3.5 billion in 1970,  We are to find at what year population of…

Q: 1. The rate of increase of a certain population of a barangay is proportional to the population. If…

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Q: A hypothetical country with a population of 20,000 people annually experiences 2000 births, 1700…

A: Given; Population Size=20,000Number of births=2000Number of deaths=1700Number of…

Q: The population of a state is known to grow at a rate proportional to the number of people presently…

A: Follow the steps.

Q: Given an interest rate of zero percent, the future value of a lump sum invested today wil always:…

A: Topic = Algebra OA. remain constant, regardless of the investment time period.

Q: If half a certain amount of radium decays in 1600 years. What percentage of the original amount will…

A:

Q: A survey estimates the current average cost of college to be $33,245per year.   ​(a) If the average…

A:

Q: 2. For a period of time, an island's population grows at a rate proportional to its population. If…

A: Let A0 be the initial population and k be the growth rate.A0 = 1174k = 6.5%  = 0.065

Q: 2. The population of a certain state is known to grow at a rate proportional to the number of people…

A: 2) Given:         Rate of increase of the population of the state is proportional to the number of…

Q: Find the capital value of a fort at a strategic location, where the annual rent is $950,000, paid in…

A: Given that the annual rent of a fort at a strategic location is $950,000 with the compound interest…

Q: If simple interest is evaluated, then the interest obtained will always be directly proportional to…

A:

Q: 2. The popu lation of certain country is known to increase as a rate proportional to the number of…

A:

Q: If the national economy shrank at an annual rate of 9​% per year for three consecutive​ years, then…

A:

Q: If population y grows at a rate proportional to the current population, then y could be

A: This make separable differential equation

Q: The population of a certain state is known to grow at a rate proportional to the number of people…

A: Given that 10 years the population has trembled and for  20years the population is 150000. p(t)…

Q: 2. It is estimated that t months from now, the population of a certain town will be changing at the…

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Q: (3) If the Nigerian population was 65 million in 1950 and 85 million in 1970, what will the popu-…

A:

Q: For a period of time, an island's population grows at a rate proportional to its population. If the…

A: The general growth formula is given by,

Q: If prices increase at a monthly rate of 3.4%, by what % do they increase in a year?

A: Annual increase = (((monthly increase+100)/100 )12 -1) 100 Hence Annual increase = ((103.4/100)12…

Q: If the value of Leo’s house goes up from $350,000 to $450,000 in the next 6 years, what was the…

A: Simple Growth percentage in the House value in the 6 years = (450000-350000)/350000 = 0.285714285 ~…

Q: 7. A radioactive material decays at a rate proportional to its amount. If the material has a…

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Q: 1. The rate at which radioactive nuclei decay is proportional to the number of such nuclei that are…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: If the population of a small city is 45,000. If the population grows at a rate of 3% per year, in…

A:

Q: It is estimated that i months from now, the population of a certain town will be changing at the…

A:

Q: A money market fund has a continuous flow of money at a rate of ​f(x)=1,900x−180x2 for 10 years.…

A:

Q: How much money should be invested at a rate of 6% compounded continuously to produce an amount of…

A:

Q: 7. At what interest rate compounded continuously must money be invested in order to triple in 10…

A: We know that  P=Aert where A= Principal value r=rate  and t=time

Q: Find the capital value of a fort at a strategic location, where the annual rent is $750,000, paid in…

A:

Q: 5. A storage battery discharge at a rate which is proportional to the charge. If the charger is…

A: Given that: Rate of discharging is proportional to the charge.Charge is reduced to 50% of its…

Q: 9. If you invest $2500 at 2.8% compounded continuously how much will you have at the end of 10…

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Q: 2. Suppose a nuclear accident releases 50 kilograms of the element Cesium 137. If the half life of…

A: Given- Intial amount of Cesium-137 is 50 kg and half life is 30 years. To find- The amount after 30…

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A:

Q: Suppose a radioactive substance has a half-life of 1000 years. What fraction will be leftafter 1000…

A: Given that the half life is 1000 years. This means 1/2 of the the original amount is left after 1000…

Q: If an initial population of 32 grows exponentially at a rate of 50% per year, then what will the…

A: Given,          An initial population of 32 grows exponentially at a rate of 50% per year.We know…

Q: A species of endangered tigers has a population in 2020 of about 900, and that number is expected to…

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

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Q: a) If an investment grows in value at 2.4% per year, how long will it take for its value to double?…

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Q: 2. The population of a suburb doubled in size in an 18-month peri growth continues and the current…

A: In this question we will use basic of calculus i.e application of differential equation. We will…

Q: 2. A radioactive material loses 25% of its mass in 10 minutes. What is its half-life?

A: Let No be the initial mass, N be remainingmass.  Then  N= No - 25100 No = No - No4=34NoHence    t…

Q: Suppose an unknown radioactive substance produces 6400 counts per minute on a Geiger counter at a…

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Q: 1. The value of a car depreciates at a rate of 12% per year. If its original cost is $12,000.00,…

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Q: If prices increase at a monthly rate of 3.2%, by what percentage do they increase in a year?

A: ANSWER :

Q: A company will need 1,500 barrels of fuel at the end of this month, and its needs will increase at…

A: Use the formula: Final quantity=Original Quantity1+Rate of increase per each time-interval100Number…

Q: If the half-life of a radioactive substance is 7,300 years, then at what rate is it decaying? (Hint:…

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.