If the half-life of a radioactive substance is 6,800 years, then at what rate is it decaying? (Hint: The amount goes from A, to A, in 6,800 years.) The decay rate, k, is (Round to six decimal places as needed.)

Q: Under laboratory conditions the half-life of ozone is approximately 25 hours. If Q =Q0ekt is the…

A: Given:- Under laboratory conditions the half-life of ozone is approximately 25 hours. If Q =Q0 ekt…

Q: Given the exponential growth function f(x) = 78(1.0145)* What is the initial value of the function?

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Q: If $6000 is invested at 3% compounded continuously, what is the amount after 8 years? The amount…

A: Answer  is   7625

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Q: Complete the table shown to the right for the half-life of a certain radioactive substance. Decay…

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Q: The radioactive isotope of lead, Pb-209, decays at a rate proport lead to decay? (Round your answer…

A: Let  at time t amount of radioactive istope is  A(t)

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

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

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Q: If $5000 is invested at 8% compounded continuously, what is the amount after 3 years? The amount…

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Q: Complete the table shown to the right for the half-life of a certain Half-Life Decay Rate, k…

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Q: Find the present value for a $90,000 investment for 24 years at a compounded continuously at 4.1%.

A: P=Aert Where P is present value , A is amount and r is rate and t is time.

Q: Suppose a sample of a certain substance decayed to 77.4% of its original amount after 300 days.…

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Q: How much should be invested now at an interest rate of 5.5% per year, compounded continuously, to…

A: We can find the answer as below.

Q: If $12, 000 is invested at a rate of 3% per year compounded continuously, find value of the…

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Q: Complete the table shown to the right for the half-life of a certain radioactive substance. ...…

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Q: How many years will it take for an initial investment of $30,000 to grow to $75,000? Assume a rate…

A: An initial investment (P) compounded continuously with a rate of interest (r) in time (t) will grow…

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

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Q: 11) The half-life of silicon-32 is 710 years. If 30 grams is present now, how much will be present…

A: Given data : Ao=30 gmp =710 years t= 300 yearsLet "A" be the amount after 300 yearsA=?

Q: 5b. How long, to the nearest tenth of a year, will it take $8000 to grow to $16,000 at 8% annual…

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Q: what is the​ half-life of a radioactive​ element, which decays according to the function…

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Q: An initial amount of $1900 is invested in an account at an interest rate of 8% per year, compounded…

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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: At what nominal rate compounded continuously must money be invested to double in 6 years? A rate of…

A: We will solve the problem

Q: A bank offered 1 3/4% interest on savings accounts compounded continuously. -How much is a $5,000…

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Q: If the half-life of a radioactive substance is 5,200 years, then at what rate is it decaying? (Hint:…

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Q: Consider the following investment options. Option 1: invest $4000 for 8 years at 8% compound…

A: Option 1: Given Investment of $4000 for 8 years at 8% compounded annually. When it is compounded…

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

A: An investment P compounded continuously at a rate of interest of r % per year for t years…

Q: At what interest rate compounded continuously must money be invested to triple in 6 years? A rate…

A: Continuously interest compounded formula is P(t) =Po ert

Q: A sample of bacteria is decaying according to a half-life model. If the sample begins with 500…

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Q: If $6,000 is invested at 3% compounded continuously, what is the amount after 7 years? The amount…

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Q: Charlie wants to buy a bond that will mature to $5000 in seven years. How much should he pay for the…

A: The maturity amount, A = $5000 The rate of interest, r = 2% = 0.02 Time, t = 7 years To evaluate:…

Q: If $12, 000 is invested at a rate of 3% per year compounded continuously, find value of the…

A: The formula for continuously compounded interest is, A=Pert where P is the principal amount, r is…

Q: In 1798 the English political economist Thomas R. Malthus claimed that, unchecked by environmental…

A: The growth rate can be evaluated as the change of the value of the function in the given time…

Q: Carson invested $2,700 in an account paying an interest rate of 1.6% compounded continuously.…

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Q: How much should be invested now at an interest rate of 5.5% per year, compounded continuously, to…

A: This question is based on formula of continuous compounding.

Q: A certain loan program offers an interest rate of 6.5%, compounded continuously. Assuming no…

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Q: If the half-life of a radioactive substance is 6,700 years, then at what rate is it decaying? 1…

A: The decay law is given by, A(t)=A0e-kt Where, A0 is the amount at t=0. And, t1/2=ln2k

Q: What parameter is this question asking for? What deposit made at the end of each month will…

A: Given data: Future value FV =$10000, number of periods n=5*12 =60 Periodic rate of interest r = 4%…

Q: 16) How long, to the nearest year, will it take an investment to triple if it is continuously…

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Q: How much money must be invested now at 10% interest compounded continuously so that $120, 000 will…

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Q: 4. A deposit of $400 is made in an account that earns interest at an annual rate of 2.5%. How long…

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Q: How much should be invested now at an interest rate of 6.5% per year, compounded continuously, to…

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Q: Suppose a sample of a certain substance decayed to 79.6% of its original amount after 300 days.…

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Q: If you invest $20,000 at 7% interest compounded continuously, what is the average amount in your…

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Q: The half-life of Carbon-14 is 7 years. How much of an initial 169 g sample will remain after 28…

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Q: How long will it take for an investment to triple, if interest is compounded continuously at 6%? It…

A: Given

Q: Scientists have observed that a small colony of penguins on a remote Antarctic Island obeys the…

A: We know that, P= P0ert where P is the population at time t. P0 is the initial population. r is the…

Q: At what interest rate compounded continuously must money be invested to triple in 4 years? A rate of…

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Q: How long will it take an investment of $3,400 at an interest rate of 4% per year compounded…

A: Given,       P = $3400  ( initial investment/ principal)       I = 4% = 0.04 ( interest rate)      A…

Q: At what interest rate compounded continuously must money be invested to double in 9 years? A rate of…

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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.