15. pot INSTRUCTIONS: A bacteria culture grows with a con- stant relative growth rate. The bacteria count was 400 after 2 hours and 25600 after 6 hours. (a) What is the relative growth rate? (b) What was the initial size of the culture? (c) Find an expression for the population of bacteria after t hours (d) Find the number of cells after 4.5 hours (e) Find the growth rate at time t = 4.5 hours (f) When will the population reach 50,000 cells?

Q: lane flying horizontally at an altitude of 2 miles and a speed of 450 mi/h passes directly over a…

A: Given query is to find rate of change of distance.

Q: Let F(x) = f f(t) dt, where f is the function whose graph is shown. 3+

A: Given: The graph of f is the following. For the function F(x) to have maximum, we must have…

Q: Find the volume of the solid generated by revolving the given region with its boundaries about the…

A:

Q: Use the guidelines of curve sketching to draw the graph of y = x(x − 4)³

A:

Q: 22. Find the point on the curve y = √x that is closest to the point (3, 0).

A:

Q: Given f (9) = 2, f' (9) = 6, g (9) = -1, and g' (9) = 8, find the values of the following. (a) (b)…

A: to find the values.

Q: OA, OB and OC, with O as the origin, are three mutually perpendicular lines whose direction cosines…

A:

Q: The function f(x) = 2x - √x if x ≤ 1 x²-1 x-1 2 if 1<x<2 Select one: O True False if x22 is…

A:

Q: Find and prove the limit or deteremine if the limit doesn't exist: arctan(n)

A:

Q: The following differential equation can be reduced to the linear equation by the 1 substitution u =…

A:

Q: 1. INSTRUCTIONS: Differentiate the following func- tions (respect to a) using any method. (a) f(x) =…

A:

Q: Find the volume of the solid obtained by re -e region bounded by the graphs of y=x²+²x+1 y=1-x…

A: y = x2 + 2x + 1 y = (x + 1)2 This function is a parabola with its vertex at (-1, 0). Line is y + x…

Q: 1: Consider the differential Question 1. equation : y cost + 2te" + (sint + t²e³ - 1)y' = 0. a) Show…

A: A differential equation of the form M(t,y)dt+N(t,y)dy=0 id said to be exact iff, ∂M/∂y= ∂N/∂t

Q: The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest…

A:

Q: Determine whether the statement is true or false. ln a − ln b = ln(a − b) for all positive real…

A: Determine whether the statement is true or false. ln a − ln b = ln(a − b) for all positive real…

Q: Fill in the missing form of the equation. Exponential Form ex + 2 = 14 Logarithmic Form ln(x + 11) =…

A:

Q: 8) The volume of the solid generated by revolving the region bounded by 3π 5Tt y = cos x, y = 0,…

A:

Q: In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the…

A:

Q: Without​ graphing, determine whether the following equation has a graph that is symmetric with…

A:

Q: Use a triple integral to find the volume of the given solid. The solid enclosed by the paraboloids y…

A: solid is enclosed by the curve y=x2+z2   , y=72-x2-z2

Q: The equation 2 dy x² dx is a first-order linear differential equation. Select one: O True O False -…

A:

Q: If f(x, y, z) = xe² sin (42), then the gradient is Vf(x, y, z) =

A:

Q: Find f'(16) if f(x) = 7x² + 3x +3 √I

A: To find the derivative of given function

Q: A Norman window has the shape of a rectangle surrounded by a semicircle (thus the diameter of the…

A:

Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x) =…

A: To solve the following problem of finding the volume

Q: Find dy/dx. y=9x-5

A: y=9x-5

Q: Find the critical points in the domain of the function: y=4-x³-3 -3.x. If there are no critical…

A:

Q: 4- Find du &f z=e Zsin (XJ) X=t_y= int.

A:

Q: Find the Taylor polynomial p3(x) for f(x) = 5x¹/³ at x = 3.

A:

Q: (5y²+3 x)dx+7 xydy=0 (*) a) Determine whether the given differential equation (*) is exact SM-Nx -dx…

A:

Q: Find the follow indefinit x5 dr.

A:

Q: A rectangle is to be inscribed in a semicircle of radius 2. What is the largest area the rectangle…

A: We have to use a concept of derivatives

Q: Coefficients Linear in Two Variables Obtain the particular solution when x=3 and y=7: (x + y −4)dx -…

A:

Q: Find the coordinates of the point (x, y, z) on the plane z = 2 x + 3y + 2 which is closest to the…

A:

Q: Indicate a function for which 1 1 | 1 (2) de = 2/1 (2) de f(x) f -1 0 ○f(x) = ex f(x) = x cos(x)…

A: Given query is to find the correct option for the integral.

Q: Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter…

A: We have to find the vertical and horizontal asymptotes.

Q: Evaluate Your Answer: Answer [₁¹ 1 - 3x √x dx

A:

Q: The integrating factor of the following first- order linear differential equation is Select one: O…

A:

Q: Find the critical points in the domain of the function: y=tan(x) . If there are no critical points,…

A:

Q: Find an equation of the line tangent to the graph of ​f(x)=2/x at (6,1/3).

A:

Q: Differentiate. y' = || y = eP(p + p√p) X

A:

Q: Express f(x) in the form f(x)=(x-k)q(x) +r for the given value of k. f(x)=x³+4x²+6x +4, k = -2

A:

Q: Let f(u)=u^3 and g(x)=u=6x^4+2. Find (f o g)'(1).

A:

Q: erentials and first approximations nd first approximations to the expressions below, and compare…

A: Solution of the problem as follows

Q: Find equations of the tangent plane and normal line to the surface x = 2y² + 4z² 354 at the point…

A:

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m³/min. How fast is the…

A: Let's find height of the water increasing rate.

Q: In order to solve the following Bernoulli's equation dy dx we use the substitution e+3 Select one:…

A:

Q: Using a proper substitution, Bernoulli's equation dy dx will be reduced to the linear differential…

A:

Q: Consider the function g given by g(x)=|x−6| +2.   ​(a) For what​ x-value(s) is the function not​…

A: A function is non-differentiable when there is a cusp or a corner point in its graph.   Given :…

Q: = 1 y' + ²y = ∙y' + a) Is the given differential equation nonlinear? Is it a Bernoulli's equation?…

A: