if y = 5/2[e^x/5 + e^-x/5], the show that y,, = y/25

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: 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

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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 derivative of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: 2) 12

A:

Q: What is the total amount of 4500 TL with 3,7 % continuously compound interest after 3 years?

A: Given Present value (P)= 4500 TL Rate (r)=3.7% Number of years (t)= 3

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Q: ind the half-life of a radioact

A: Given that: Rate = 12 %

Q: how long will take for an investment to double in value if the interest rate 3% APR compounded…

A: We have A(t) = 2A(0) and r = 3% = 0.03

Q: Find the effective rate of interest.For 5% compounded continuously

A: Here we have to find the effective rate of interest. For 5% compounded continuously.  r = 5%…

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

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

Q: The rate of a continuous money flow starts at $1000 and increases exponentially at 5% per year for 4…

A: We use the formula                                P = ∫0T f(t)e-rt dt

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…

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A:

Q: (5) log yz (6) log (7) log (ry) (8) log rvz

A: We will find the value of these problem using logarithm formula.  We know  , log(A/B) = log(A)  -…

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A: We will take the logarithm with base e and then find the derivative with respect to x and then…

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A: While calculating compound interest, the addition of interest to the principal sum of a loan or a…

Q: 5th derivative of y = log x^5 to the base 2

A:

Q: Suppose the population of a city has been growing at a rate of 2.5% per year for each of the last 8…

A:

Q: Express in terms of sums and differences of logarithms. 2 In In 3 3x y 2 3 3x y

A: Given:ln23x3ywe need to express this logarithm in terms of sums and differences.We know thatln (ab)…

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: The accumulated amount of P8000 is P10000 after 2 years, calculate the interest rate if it is…

A: The accumulated amount of $8000 is $10000 after 2 years,   We have to calculate the interest rate…

Q: find the derivativey=log(to the 4th) time (2x Third -6x)

A: To apply the rules for derivative of composite functions

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

Q: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: $400 invested at 7% compounded continuously after aperiod of 3 years

A:

Q: The rate of a continuous money flow starts at ​$600 and increases exponentially at 4% per year for…

A: Given, Initial amount P0 = $600 R = 4% = 0.04 T = 15 years

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

A:

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…

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A:

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Q: Suppose there is one pupil in a class of 60 who was infected by the Influenza B virus. Assuming none…

A: The logistic growth equation here is: P(t)=P0e0.7050t Where, P is the number of students inflected…

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Q: Interest is compounded continuously at 5%.  How long until a $5000 investment grows to $12000?

A: Interest is compounded continuously at 5% $5000 investment grows to $12000

Q: A quantity with an initial value of 8200 grows continuously at a rate of o.55% per decade. What is…

A:

Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A: Topic-basic maths

Q: 4. The population of Lalaland is 600,000 currently and is expected to grow (continuously) at 3.5%…

A: The present population P =600,000 Growth rate r = 3.5 % per year To find population after time t =…

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: see attached

A:

Q: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

A: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

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

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Q: What initial investment at 8% compounded continuously for 5 years will accumulate to $50, 000?

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Q: Use a linear approximation to estimate log10(10.5).

A:

Q: How long does it take to have a balance of $900 if $500 is invested at 0.75% annual interest…

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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: 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: A quantity with an initial value of 3600 grows continuously at a rate of 2.5% per decade. What is…

A:

Q: Suppose you deposit 3 000 at a 6% interest compounded continuously. What will the Average value of…

A: Given Deposit =$3000 Interest=6% Compounded continuouslyA=Pert