A quantity of a radioactive material decays to half of the original amount in 5 seconds. How long will it take for the amount to decay to 1 32 of its original amount? Simplify your final answer.

Q: The population of a city was at 6,000 people in 2001. If the population grows at a rate of 1.7% each…

A: Given the population city was 6000 people in 2001. If population grows at a rate of 1.7% each year.…

Q: In the last ten years, the population of Brazil has grown at an exponential rate of 0.8% per year to…

A: In the last ten years, the population of Brazil has grown at anexponential rate of 0.8% per year to…

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: How long will 2 million pesos earn a simple interest of 200, 000 at 1% per annum

A: The formula for the simple interest is given by S.I= PRT  where S. I is the simple interest , P is…

Q: Suppose a particular antibiotic that is introduced to a petri dish containing 3000 newly discovered…

A: Introduction: Recurrence relation is very important in discrete mathematics. It relates a term with…

Q: The population of Watesville decreases at a rate of 1.6% per year. If the population was 62,500 in…

A: Given: Population in 2014, P = 62,500 Rate of decrease, r = 1.6% Population in 2020, Q = ?   Number…

Q: Suppose Elizabeth takes a 700 mg dose of ibuprofen and every hour that passes the amount of…

A:

Q: A machine that drills holes for wells drilled to a depth of -72 feet in one day (24 hours). At this…

A: Given Machine drills holes for wells to a depth of -72feet in 24 hours we have to find how many…

Q: May is 5 years older than June. 7 years ago, May was two times as old as June. Find their present…

A: To convert the given word problem into equations and find the unknown ages

Q: A boat costs $10,800 and decreases in value by 6% per year. To the nearest penny, how much will the…

A: Costs of boat after 7 years is $7003.55 .

Q: of the Philippines has doubled in the last 50 years. The population of the Philippines in 1948 was…

A:

Q: Researchers recorded that a certain bacteria population declined from 290,000 to 300 in 24 hours. At…

A: Bacteria in 16 hours=?

Q: The number of people living in Canada rose by 1.2% to 38.5 million in 2021. If this population…

A:

Q: The half-life of radioactive cobalt is 5.27 years. If 100 grams of radioactive cobalt is present…

A:

Q: Richard invests $184.67 every month into his 401k. At the end of 30 years, he has a balance of…

A:

Q: The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are…

A: Given: The half-life of the radioactive element krypton-91 is 10 seconds.

Q: An car depreciates (decreases in value) by 20% of its value from the previous year. If the car was…

A: Price of the car is decreases by 20% for every year. Therefore r=20% Price of car is $40,000…

Q: You inherited a house worth $650,000 today. If the value increases by 4% each year, what would the…

A: given: we inherited a house worth $650,000 today. If the value increases by 4% each year, we have to…

Q: A population of 10 hamsters will triple every year. What will be the population after 7 years?…

A: Given: A population of 10 hamsters will triple every year…

Q: The size of the beaver population at a national park increases at the rate of 5.1% per year. If the…

A: Given query is to find population of beaver after 4 years.

Q: The half-life of radioactive potassium is 1.3 billion years. If 10 grams is present now, how much…

A:

Q: Ana is five years older than Beth. In five years, the product of their ages is 1.5 times the product…

A: Given problem:- Ana is five years older than Beth. In five years, the product of their ages is 1.5…

Q: Suppose that a car’s worth depreciates at a constant rate.  You bought the car in 2002 for $18,000…

A: Considering the years as x-axis and and cars worth as y-axis. Let 2002 be 0. Therefore,the given…

Q: After 100 years, 1/32 of the original amount of a substance remains. What is the substance…

A:

Q: a radioactive isotope, selenium, used in the creation of medical images of the pancreas, has a…

A: To use the exponential model of radioactivity to determine the required amount of substance

Q: How many years will it take P50,000 invested at 8% simple interest to double to P100,000? How long…

A: Given, r=8%=0.08, F=2P, where F is the final amount double of P i.e. principle amount n= number of…

Q: A car was bought for $85,000. It was sold 10 years later for $20,500. At what yearly rate did it…

A:

Q: The cost of a car decreases by 10.2% every year. If the estimated resale value after 15 years is…

A:

Q: Invested at 6% interest, ₱10,000 today would be worth approximately ₱20,000.00 in ___ years.

A: Given information Principal P=$10,000 Interest I=$20,000 Interest rate r=6% We have to fin the time.…

Q: In the last ten years, the population of Brazil has grown at an exponential rate of 0.9% per year to…

A: Present population = 204,832,665Rate of growth = 0.9% per yeartime = 10 years

Q: The half-life of a medication prescribed by a doctor is 6 hours. How many mg of this medication is…

A: The medicine is decaying exponentially. Use the half-life formula to calculate the medicine left…

Q: When a petroland oil well was first brought on line, it produced 1,900 barrels of crude oil a day.…

A: Petrol and oil well produced  In the first year , production is 1900 barrels of crude oil per day.…

Q: The​ half-life of caffeine in a​ person's bloodstream is about 6 hours. If a​ person's bloodstream…

A: The formula for half-life:

Q: Anton is 4 years older than Liza. The product of his age three years from now and Liza's age two…

A:

Q: $14,000 is invested for 25 years, what will be the ending balance if interest is 8% compounded…

A:

Q: The 1990 earthquake in Dagupan City had a magnitude of 6.9. While the 2013 earthquake that occurred…

A:

Q: The population of a city is 168,000. The population declines by 2.6​% every​ year, what will the…

A: It is given that:

Q: A substance has a half-life of 2.045 minutes. If the initial amount of the substance was 132.8…

A: Use the formula for the amount remaining after n- half lives of a radioactive substance.

Q: The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain…

A: To find the remaining amount after 4000 years.

Q: The half-life of Sodium-24 is 14.96 hours. If a sample contains 490 mg, how many mg will remain…

A:

Q: How long will it take for an amount to double its value if invested at 9.3% simple interest?

A:

Q: The size of the wolf population at Isle Royale National Park increases at a rate of 4.3% per year.…

A:

Q: One type of chromium has a radioactive decay rate of 2.5% per day. If 20 pounds of this chromium is…

A:

Q: If a country with a growth rate of 2.8% can double its population size in 24 years, then how long…

A: If a country with a growth rate of 2.8% can double its population size in 24 years, then how long…

Q: Two years ago there were 7 grams of a radioactive substance. Now there are 5 grams. How much will…

A: We have to represent the first order decay.

Q: The halflife of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after…

A:

Q: In 1980, direct U.S. business investment abroad was about 13.5 billion dollars. From 1980 through…

A: Initial investment = 13.5 billion dollar rate = r =0.1124 t = time Exponential model y=13.5e0.1124t

Q: A $25000 investment has grown by 11% annually since January 1, 2020. When will the investment reach…

A: A $25,000 investment has grown by 11% annually since January 1, 2020. When will the investment reach…

Q: y one half every 3 years. How long, to the nearest tenth of a year, would it take for the value of…

A:

Q: A car is purchased for $31,000 . Each year it loses 30% of its value. After how many years will the…

A: Let the depreciated amount be represented by D(t). then according to the given condition.

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.