what is the​ half-life of a radioactive​ element, which decays according to the function ​A(t)=A0e^−0.0132t​, where t is the time in years. round to the nearest tenth

Q: find the decay constant

A: In this question, to find the decay constant by using the formula obtained with the help of the…

Q: Suppose that $8000 is invested at an interest rate of 5.2% per year, compounded continuously. What…

A: Principal= P= $8000 Interest rate = 5.2%= 0.052 Final amount = double of 8000=16000

Q: How long, to the nearest year, will it take me to become a millionaire if I invest $3000 at 9%…

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Q: The half-life of Erbium-171 is 7.5 hours. What is the hourly decay rate? Express the result to four…

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Q: sketch the shifted exponential curves

A: We have to sketch the shifted exponential curves: y=-ex and y=-e-x. We know the graph of ex and e-x,…

Q: Find the effective rate of interest. For 6% compounded continuously

A:

Q: What is the total amount of 24000 TL with 4,8 % continuously compound interest after 5 years?

A: Consider the formula for continuous compounding, A=P·er·tHere,P=principalr=rate of interestt=time…

Q: Find the First Derivative: y=log10(5x+3/5x-4)

A:

Q: ind the half-life of a radioact

A: Given that: Rate = 12 %

Q: Find the present value of $4000 payable at the end of 4 years, if money may be invested at 6% with…

A:

Q: Find the compound amount if $12,104 is invested at 6.2% compounded continuously for period 3 years

A: The formula used: A=Pert

Q: The half-life of carbon-14 is 5700 years. If an item is discovered with only 17% of the original…

A: Given Half life of carbon-14 =5700 years  i.e. and an item is found with only 17% of the original…

Q: A quantity with an initial value of 480 grows exponentially at a rate such that the quantity doubles…

A: Here a value is increasing exponentially. We need to find the value after specified time.

Q: Consider a population of a certain country that is observed to grow exponentially. Based  from the…

A:

Q: A quantity with an initial value of 840 decays continuisly at a rate of 5% per day. What is the…

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Q: How long, to the nearest year, will it take an investment to double if it is continuously compounded…

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Q: If the present value of $1000 to be received in 5 years is $559.90, what rate of interest,…

A:

Q: What rate of interest compounded continuously will yieldan effective interest rate of 6%?

A: It is given that, the effective interest rate is 6%. re=6%=0.06

Q: If there are 520 grams of Tadioactive material with a half-life of 12 hours, how TIuch of the…

A: The material is decaying at a constant rate, every 12 hours it is getting halved.  So, it is an…

Q: Find the compound amount if $12,104 is invested at 6.2% compounded continuously for each period.2…

A: Given: P=12,104  dollarsr=0.062t=2  years

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: Formula to calculate continuously compounded interest: A = Pert where, A is Amount at time t,P =…

Q: $5,000 is invested in an account earning 6% interest (APR), compounded continuously. How much is in…

A: Total investment P=$5000 Rate of interest R= 6% Time t=3 years Total amount after 3 years

Q: Find the compound amount if $12,104 is invested at 6.2% compounded continuously for period 4 years.

A: Given : Invest amount ( P ) = $ 12,104 . Interest rate ( r) = 6.2 %  Period ( t) = 4 years

Q: Determine the half-life of a particular element if 200gr of that element decays to 15 gr in 12…

A: Given: 200 gr of an element decays to 15 gr in 12 hrs. To find: Half-life of an element.

Q: A certain specimen of charcoal contains 55% of Carbon – 14 as compared to a charcoal at present day.…

A: Given- X=X0e-kt  and the charcoal contains 55% of carbon as compared to present day and the value of…

Q: Find the time needed to double an investment at 8% annual interest rate compounded continuously.

A:

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: If the quantity of a substance decreases by 4% in 11 hours, find its half-life. Round constants to…

A: Let initial quantity is A0 . Quantity after t hours = Ak= some constant.A is given by:

Q: The half-life of Cesium-137 is 30.7 years. How long will 200 grams of Cesium-137 take to decay to…

A: Given data The half-life of the cesium-137 is t1/2 = 30.7 years. The initial amount of the…

Q: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. What is the…

A: Given: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. To…

Q: Suppose the rate of net investment is given by I (t) = Lnt, find the total capital accumulation…

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Q: How long to the nearest year will it take $50,000 to triple in values at7.5% annual interest…

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Q: A material decays at the rate of 0.099% per year. How long will the material take so that only 30%…

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Q: find the present value of an investment worth $15,000 in 15 years with 5% interest compounded…

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

A: We have to find the growth rate.

Q: Suppose that the half-life of a substance is 250 years. If there were initially 100 g of the…

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Q: Suppose the half-life of a certain radioactive substance is 20 days and that there are5 grams…

A: Given that, The half-life of a certain radioactive substance is 20 days and that there are 5 grams…

Q: Mr. Reyes places 100,000Php in a time deposit which pays nine percent per annum compounded…

A: topic - exponential function

Q: An Asian country had a population of about 0.90 Billion people in 1995 and a growth rate of 1.3% per…

A: *** This is the problem related to financial mathematics and we are advanced math expert and have…

Q: A quantity with an initial value of 2000 grows exponentially at a rate of o.35% every 2 days. What…

A: Given, A quantity with initial value of 2000 grows exponentially at a rate of 0.35 % every 2 days We…

Q: What is the exponentially smoothed value for period 4, using a smoothing constant of 0.4?

A: Given that  Time series data  Observation  Value 1 10 2 15 3 18 4 12 5 20 6 21 7 21…

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: We can find the required year in the following steps.

Q: A quantity with an initial value of 8200 grows continuously at a rate of 0.55% per decade. What is…

A: Initial Value=  8200. Growth rate= 0.55% . We can formulate the following equation for "t" years :…

Q: A sample of a newly discovered element, West Virginium, has been discovered. A 648 mg sample has…

A:

Q: Find the compound amount if $12,104 is invested at 6.2% compounded continuously for each period 4…

A: A= P ert

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

A:

Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

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

A:

Q: The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year)…

A: The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year)…

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.