The number of bacteria, per unit of volume, existing in a culture after x hours [0, 1, 2, 3, 4,...] is shown in the table:   Fit data to curves y=ab^x y=ax^b compare the values obtained using these equations with the experimental data and comment on what you observed. State which mathematical model best represents this data.

Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

Q: The measurements of the base and altitude of a triangle are found to be 36 and 50 centimeters,…

A: Let base= B  Altitude= H Given that B= 36 , H=50 , dB=0.25 , dH=0.25

Q: A circular plate is measured to have a diameter of 3.5 feet if the measurement could be off by as…

A: Given, The diameter of the circular plate,d=3.5feet The radius of the circular…

Q: A tin can has a circular base of radius 2 inches and height of 6 inches. If the thickness of its…

A: We have to find the volume of tin can using differentials.

Q: A hemispherical dome of radius 40 feet is to be given 3 coats of paint, each of which is 1/100 inch…

A: To estimate the amount (volume) of paint needed under the required conditions

Q: The dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters, and 60…

A: Given: The dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters and…

Q: Each side of an equilateral triangle measures 3 cm, with a possible error of 0.1 cm. Using…

A: This question is taken from the differentiation in which we have to find the relative error in the…

Q: Find a curve through the point ( 1 , 5/6 ) whose length on the interval [ 1 , 2 ] is given by ∫ 1^2…

A: The length of the curve y=f(x) from x=a to x=b is L=∫ab1+dydx2dx Now , Length of a curve on the…

Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

A:

Q: Find the slope and y-intercept of the line through the point (9,5) that cuts off the least area from…

A: Equation of line : Y - y = m(X-x) If this passes through point(9,5) Y-5 = m(X-9) Y = m(X-9)+5 X…

Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

A:

Q: A boundary stripe 3 in. wide is painted around a rectangle whose dimensions are 100 ft by 260 ft.…

A: Please see the explanation below

Q: Find the slope and y-intercept of the line through the point (1,5) that cuts off the least area from…

A: In the question we have to find slope of line and y-intercept.

Q: A hemispherical dome of radius 40 feet is to be given 11 coats of paint, each of which is 1/100 inch…

A: The volume of Hemisphere = 23πr3 Differentiate with respect to r…

Q: A point moves along the curve y = √x in such a way that the y-value is increasing at a rate of 2…

A:

Q: rectangular parallelepiped with an altitude of 10 cm have its width decreasing by 2 cm/min and…

A: Topic:- application of derivatives

Q: A boundary stripe 3 in. wide is painted around a rectangle whose dimensions are 140 ft by 200 ft.…

A:

Q: An open cylindrical tank is to have an outside coating of thickness 2cm. If the inner radius is 6cm…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – axis…

A: Solution

Q: Find the general solution using Integrating Factors Found by Inspection

A:

Q: Find the slope and y-intercept of the line through the point (6,6) that cuts off the least area from…

A: Given : Point (6,6)

Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: At a certain moment, an object in linear motion has velocity 100 m/s. Estimate the distance traveled…

A: Given that: At a certain moment, an object in linear motion has velocity 100 m/s To estimate the…

Q: A rectangular parallelepiped with an altitude of 10 cm have its width decreasing by 2 cm/ min and…

A:

Q: A coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of edge 30…

A: Given that a coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of…

Q: A circle has a radius of 5 cm, if the radius is increased by 0.1 mm., what is the estimated increase…

A: Let's find.

Q: A square is measured and each side is found to be 8 inches with a possible error of at most 0.01…

A: We are given that each side of a square is 8±0.1. Let x be the side of square and then the side of…

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: A researcher for a tire company has collected data about the stopping distance in feet for different…

A: The data values are in the range of 59 to 74. As a result, the bottom limit of the range is supplied…

Q: The process of using variables to represent unknown quantities and then finding relationships that…

A: The process of using variables to represent unknown quantities and then finding relationships that…

Q: a hemischperical dome has a diameter of 50 m. use differentials to estimate the amount of paint…

A: the problem concerns an application of differentials

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: Assume the learning rate for new skills is proportional to the difference between the maximum…

A: The learning rate for new skills is proportional to the difference between the maximum potential for…

Q: A hemispherical dome with a diameter of 60 meters has to receive a coat of 5 cm of paint. Use…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: A hemispherical dome of radius 30 feet is to be given 11 coats of paint, each of which is 1/100 inch…

A:

Q: Express the mathematical relationship between stress and strain in case of elastic material.

A: The mathematical expression can be related as:

Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 18 cm high and…

A:

Q: The two legs of a right triangle are measured as 5 m and 12 m with a possible error in measurement…

A:

Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

Q: ential equation is given by

A:

Q: 6. The length of a rectangular yard is measured to be 84 feet and the width to be 36 feet. If the…

A:

Q: An ice cube melts in the sun, causing it to shrink. Use a linear approximation to estimate the…

A: The length of the side of the ice cube changes from 1 inch to 0.9 inch The decrease in the side of…

Q: Find the slope and y-intercept of the line through the point (2,7) that cuts off the least area from…

A:

Q: Use a linear approximation to estimate V8.05.² Show relevant work to explain your reasoning.

A: Linearization: If y = f(x) is differentiable function at x = a, then linear approximation at the…

Q: The possible error involved in measuring each dimension of a right circular cylinder is ±0.05…

A: r=3 cmh=10 cm Error involved in measuring each dimension of a right circular cylinder is ±0.05 cm.…

Q: Find the cubic function y = ax³ + bx² + cx + d where its graph has horizontal tangent line at (-2,6)…

A: solve the given problem.

Q: Find the average rate of change of between the points on the function whose coordinates are (1, 3),…

A: Given points are (1, 3) and (2, 16).

Q: The process of using variables to represent unknown quantities and then finding relationships that…

A: The process of using variables to represent unknown quantitities and thenfinding relationships that…