Find y' of y = log5(4x + 3)

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: Solve th equation for x. log2(log3 x) = 4

A: Consider the given: log2log3x=4Using log Rule:logap=n is equivalent to p=an,log2log3x=4…

Q: Find the effective rate of interest.; For 4% compounded continuously

A: 4% compounded continuously.

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

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Q: find the derivative using logarithm of y= (x+2)^2

A: Take ln on both sides Then differentiate both sides with respect to x

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: Jay and John used to travel together but because of the pandemic, they decided to go separately…

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Q: How long (in years) will it take a $200 investment to be worth $300 if it is continuously compounded…

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Q: x+1

A: By using the formula you can solve the given problem as follows :

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

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

Q: How much should be invested at a rate of 7% coumpounded continuously to produce an amount of $15,000…

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Q: Find the derivative of y =log2x

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Q: 1) loga(3-1ogalx-)=2

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Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: How long does it take for $350 to grow to $840 at 6% annual percentage rate compounded continuously…

A: Continuously compounded interest formulaA= PertP = the initial principlee = natural baser = annual…

Q: The mass reaches 75 grams after t= years.

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Q: find derivative y=square root of (1+ x times e^-2x)

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

A: To apply the rules for derivative of composite functions

Q: How long will it take to triple $12000, invested at 4.5% compounded continuously? (A = Pe*t) %3D

A: We are given the initial value to be $12000 and rate r = 4.5% = 0.045. Now, we need to find that how…

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: tan s) Differentiate f(x) = 5* log3 %3D csc 2x

A: Consider the function fx=5xlog3tan-1xcsc2x Here, the objective is to differentiate the function.

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

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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: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

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Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5) without a calculator

A: Given equation is :Moving all the logarithm terms and using the property: ln(a) – ln(b) =…

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…

Q: Find the derivative of the function. f(x) = 2x2 In 2x f (x)= 2x[1+2 log(2x)]

A: fx=2x2ln2x

Q: 2. y=cot1-2x 3. y=log22x*

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Q: The decay constant for carbon-14 is 0.00012, with time measured in years. A piece of papyrus…

A: Decay of any radio active substance follow first kinetics and the equation of first order kinetics…

Q: State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the…

A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

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Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: What are the blanks?

A: Note: We are authorized to answer three sub-parts at a time. Since you have asked more than three…

Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

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Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Of the 1000…

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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: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) 1

A: Tangent to a curve is a line which just touches the curve and in some sense is parallel to the…

Q: Find the nth order derivative of the natural logarithm function y=lnx.

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Q: When a breeding group of animals is introduced into a restricted area such as a wildlife reserve,…

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Q: If 26 grams of radioactive waste reduces to 19.35 grams of radioactive waste after 1120 years, then…

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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…

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Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below:…

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Q: You invest 10,000  and pay 3% interest compound continuously . How will you have in 5 years?

A: Given that You invest 10,000 and pay 3% interest compound continuously .  Now we have to find amount…

Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: he radioactive isotope gallium 67 has a biological half-life of 36 hours. If re start with 100…

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Q: Find the derivatives of x log x.log(logx)

A: We have to find the derivative of-  x logx.log(logx)

Q: What is the derivative of log (x²)? ○ 2x-log(x²) 1 x² 2x O log(2x) O exp(2x)

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Q: At the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: Here, the exponential model is given by: P(t)=a×bt...(1) where P(t) is the number of cases after a…

Q: Find the time it takes for $5,800 to double when invested at an annual interest rate of 5%,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…