What is the closest value to the instantaneous rate of change of the following function at x 2? f(x) = 3 log2(x- 1) +3 %3D O-_3 log 2 log 2 1 log 2 log 2

Q: Over 4 years, researchers studied the growth of a fish population and found its growth rate to P'(t)…

A: hintddxtan-1x=11+x2 or,∫11+x2dx=tan-1x

Q: 1) Use DESMOS to graph Y = log(x – 3), show critical points. %3D

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Q: A culture of yeast grows at a rate proportional to its size. If the initial population is 4000 cells…

A: Let's find.

Q: The simplified form of In(÷-) using logarithmic rule is yz 4ln x+ In y- In z 4 In x- In y-In z 4ln…

A: The objective is to simplify the given expression using logarithmic rule. The given expression is

Q: 4. Suppose f(x) = -3x+ log2x and g(x) = 2*. Find the AROC (average rate of change) of the composite…

A: Given the function is fx=-3x+log2xgx=2x

Q: A radioactive material is known to decay at the rate proportional to the amount present. If…

A: Given A radioactive material is known to decay at the rate proportional to the amount present.…

Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: Estimate the true percent relative error for the first derivative of the function, y = log(x? + 1)?,…

A:

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

A: Let f(x) = ln x) and g(x) = e-x Let f(x) and g(x) be positive for x sufficiently large,  a) f(x)…

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

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Q: solve: loga (4x+4)= log₂ (-7x+19) = X= AS lenter DNE if no rolution)

A: topic - logarithmic equations

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Given that , The radioactive material is known to decay at a rate proportional to the amount…

Q: Differentiate the following functions: 1. y = tan(log25x) + x. log3(sec x) 2. logyx = logxy %3D

A: We havey=tanlog2 5x +x.log3 (sec x)Let  u=tanlog2 5x     and    v=x.log3 (sec x)Now y=u+vdiff.…

Q: dx aluate: :S₁ (x+1) log(x+1) A In10 In[log(x+1)] + C 1 B -In[log(x+1)]+C In 10 O In 10 log² (x + 1)…

A: Topic:- application of integration

Q: pproximate, to 6 decimal places, the value of log2(log 99.2) by linear approximation.

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Q: What happens to the rate of change of the exponential function y = ax as a becomes larger?

A: To explain the given problem

Q: 1 (log, x)' 3x ise b =?

A:

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: 10. y = log2(3x + 1) %3D

A: We have to solve

Q: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?

A: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?…

Q: If the instantaneous growth rate of COVID19 is modeled by (limHh->0)(200t+100h). At t=5 seconds…

A:

Q: A deposit of $5000 at 4% interest compounded continuously will grow to V(t) = 5000e0.04t dollars…

A: The average value for the first 20 years is given by

Q: An environmental study of a certain community suggests that t years from now the level L(t) of…

A:

Q: Question 28 to determine the instantaneous rate of change of 3, to the nearest tenth.…

A: Explanation of the answer is as follows

Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Here we have a population of fruit flies that changes at a rate of g(t)=-4e0.04t…

Q: What is the average rate of change of log(x) on the interval [1, 10]? 1 1 10 1/9

A: Note down few values of log(x). log(10)=1 log(1)=0

Q: To three decimal places, the slope of the tangent to the curve f (x) = 5 log3 a +7, at x = 2 is:

A: Slope is defined is as differentation of function at given value of x.

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: We have to determine the time necessary for the number of bacteria to triple.

Q: A breeder reactor converts relatively stable uranium-238 into the isotope plutonium-239. After 15…

A:

Q: A deposit of $3000 at 2% interest compounded continuously will grow to  V(t) = 3000e0.02t  dollars…

A: The given function is: The average value of the function f(t) on the interval from a to b is given…

Q: Suppose that P0 is invested in a savings account where interest is compounded continuously at 3.1%…

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Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: 2 In 2 log2 x dx 7- S

A: Here I am attaching image so that you understand each and every step.

Q: Differentiate. y = 12* • log 6x d x (12*- log ex) = D 6x) = [ %3D dx

A:

Q: Find the instantaneous rate of change of g(x)=(x^3-sqrt(x))e^x+(x^5-2x+3)ln(x) when x=3. Round to…

A: The instantaneous rate of change of g(x) is:…

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

Q: What is the average rate of change of f(x)=log2x from 8 to 32. what is the equation of the seant…

A:

Q: Just as exponential functions are distinguished by their rapid rate of increase, the logarithm…

A: Consider the graph:

Q: A certain radioactive material known to decay at a rate proportional to the amount present. If…

A: let 'x' be the amount present.rate α xdxdt=kx,    where k is constant.1xdx=kdtDifferentiate both…

Q: dx Evaluate: s (x+1) log(x+1) A --In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C с = -log² (x + 1) + C…

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Q: Find d/dx(4^x). Type ln(x) for the natural logarithm function.

A:

Q: What is the linear approximation of log base 5 x at x=5

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Q: 1+logx 2. =D1. %3D 1. 196 16. Solve for x, 5-log:

A: We have to solve for x .

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Image is attached with detailed solution.

Q: Find the linearization of ƒ(x) = log3 x at x = 3. Then round its coefficients to two decimal places.

A: Given: f(x)=log3(x) at x=3