II. DIFFERENTIATION 1. (E- 2x) = A- 2 B.는-2 +2 D.-2 %3! 2x 2x-1 2. 21

Q: y = In (x* + 5)³

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Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

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Q: An animal has an initial population of No. From that initial population count, it grew to 705…

A: For population growth we can use logistic model of growth , Where growth depend on  current…

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: The differential equation modeling population growth while incorporating the carrying capacity is =…

A: Given: Growth rate is 0.1 per year. Environmental limitation is of 4600 deer. Currently there are…

Q: It is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in…

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Q: 1) Find the derivative of y =-+x-1 %3D

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Q: 4 %3D 2.

A: Consider the following equation: 4x2-5y2=4 Differentiate the above equation with respect to x:…

Q: ) The population of the world in 2015 was 9.75 billion people and was growing at a rate of 25% per…

A: Given query is to find the expression for the population after t years.

Q: Find the derivative of y=ln[x^3(x^2-5)^3/4]

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Q: 43. Find the function whose tangent line has slope (x + 1)e¯* for each value of x and whose graph X-…

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Q: Suppose income from an investment starts (at time 0) at $6000 a year and increases linearly and…

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

Q: When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104…

A: Rate of change is nothing but the change happen in any observations over a period of time. Here…

Q: Shows the derivative function of: e3x+5

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Q: 2. For a period of time, an island's population grows at a rate proportional to its population. If…

A: Let A0 be the initial population and k be the growth rate.A0 = 1174k = 6.5%  = 0.065

Q: A mathematical model for world population growth over short intervals is given by P P, e", where P,…

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

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Q: Suppose that a particular pond can sustain up to 30,000 tilapia and that the undisturbed population…

A: The logistic model is given as: dP/dt = 4(1 - P/30000)P When P = 15000, we get, dP/dt = 4(1 -…

Q: s projected that x years from now the population of a certain city will be changing at the rate of…

A:

Q: 8. Create the equation of any function where the instantaneous rate of change when x = 1 does not…

A: Create the equation of any function where the instantaneous rate of change when x = 1 does not…

Q: A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced…

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Q: Suppose an unknown radioactive substance produces 22400 counts per minute on a Geiger counter at a…

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Q: 1 What is the family of the equation y %3D quadratic exponential linear

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

A: The number N of deer present at time (t) is given by Nt=12.350.01+0.54t    .....1

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: Let ,              b → base                      h →attritude . Area of the triangle A (r) = 12bh⇒ b…

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) her shadow on the…

A: Given query is to y find the rate of change of length of the shadow.

Q: sketch the shifted exponential curves

A: To draw the graphs , first draw x and y axes . Label x for x-axis and y for y-axis . Choose some…

Q: 1. 8rd Derivative of fC x) = 4 x³ - 8x5 1

A: We will use just the basic knowledge of differential calculus to answer this question step-wise.

Q: 20 18- 16 14- 12 10+ 8- 6- 4- 2- Estimate the instantaneous rate of change at x = 3 |3D

A: We have to estimate the instantaneous rate of change at x = 3 Since ,  By graph  y(3) = 19 , y(2.90)…

Q: 5. A storage battery discharge at a rate which is proportional to the charge. If the charger is…

A: Given that: Rate of discharging is proportional to the charge.Charge is reduced to 50% of its…

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: projected that, t months from now, the population of a certain town will be growing at the rate of…

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Q: 9) Find the value of the derivative at the point (2,-18) ƒ(x) = -3xV2x + 5

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Q: 3. Find the derivative of h()= 5²°-2z-1 %3D

A: We have to find derivative

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: Solve for the second derivative of the function below 3. у%3 (х— 5)*

A: Given: y = x-54 To find: Second derivative of the given function.

Q: One method of slowing the growth of an insect populationwithout using pesticides is to introduce…

A: Given as: Females grows at a rate of  r = 0.10 Number of males S=900 Then:…

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

A:

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: Given query is to give an example of exponential and logarithmic differentiation.

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A: Given dpdt=0.068P

Q: (4) Consider the constant rate of decrease of a certain microorganism. At the start, there are…

A: We have to find the number of microorganisms that will be there after 45 seconds.

Q: find the function that gives the value of the investment as a function of t. (Round your value of k…

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Q: It is estimated that t months from now, the population of a certain town will be changing at the…

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Q: It is projected that x years from now the population of a certain city will be changing at the rate…

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Q: When the interest on an investment is compounded continuously, the investment grows at a rate that…

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Q: Rank the functions x100, ln x10, xx, and 10x in order of increasinggrowth rates as x→ ∞.

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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: 2. The instantaneous rate of change of g(x) is the same for every real value of x. What conclusion…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.