Bacteria are reproducing in concentric rings in a petri dish. The circular area occupied by the bacteria is increasing at a rate of 4 cm^2/day. Find the rate of change of the radius of the circular area when the radius is 5 cm. (A = πr^2)

Bacteria are reproducing in concentric rings in a petri dish. The circular area occupied by the bacteria is increasing at a rate of 4 cm^2/day. Find the rate of change of the radius of the circular area when the radius is 5 cm. (A = πr^2)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 1SE: Can the average rate of change of a function be constant?

See similar textbooks

Related questions

Q: The function x2 f(x) 1 - x | has a local maximum when x = 2. Select one: True OFalse

Q: y? Let f(x,y) : (a) Find the domain and range of f. (b) Draw a contour map of f for k = –3, –2,…

Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y =…

Q: Find the domain and the vertical asymptotes, if any, of the following function x²-3 x²+10x+21° O a.…

Q: Find the derivative of the function. Vs - 3 f(s) = Vs +3 %3D

Q: blc (x-) got cancelled out »PW-x(x-1) (x+) 7. For what value(s) of c is f(x) = 4- x°, cr2 + 13 x <…

A: Solving

Q: 3. Evaluate: lim X-0 \sinx 4. Using the binomial series, find the power series of f(x) =

A: We have to find the limit of a function and find the expansion of 1/x

Q: hey got wrong answer still

A: Here, given that: y=x4+2, x=-3, ∆x=0.01

Q: Choose the correct graph for y = cos x with the domain indicated: y= cos x, -2Asx<

A: Given, y= cos x -2pi<=x=0

Q: fex) = I+ sinu x f(x) = 1T fcx) =-15 * sinux - secos4X %3D = -15 e sin4X- se"cos4X mL

Q: Find the first three terms of the expansion (4 – 2x). 4°(1- 폴 + 쫄 +…) O b. 2°(1 + 꼭 + 플 + …) Oc…

Q: (d) , 2x Vx2 + 2 dx -5 (e) Si J5-y dy

Q: Use the Chain Rule to find dw/dt. w = xey/z, x = t5, y = 1 − t, z = 3 + 7t

A: To find out dw/dt.

Q: e definite integral o5 tan(x)dr using strips of width for the trapezium rule correct to three…

Q: Express the vector 2u + 5w in the form v = v,i+v2j+ V3k if u = (4, - 5, 2) and w= (-3, 2, - 4). 2u +…

Q: 7-10 Evaluate the double integral. 7. y? dA, D= {(x, y) | –1< y< 1, -y – 2 < x < y} D y 8. dA,…

A: Let's find.

Q: Find and classify all the critical points of f(x, y) = 2x - 9y - xy + x2 + 5y2 .

Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

Q: What are intervals of concavity of the function f(x) = 2x - 6x² – 3 ? Concave upward on (1, o) and…

Q: I cant figure out your process and answer

Q: (i) What are the projections of the point (2, 3, 5) on the ry-, yz- and rz-planes? (ii) Write…

Q: Show that the particular solution of the differential equation dy 5dy + 6y = 12(x+e") dx dx dy is y…

Q: The graphs of the first and second derivatives of a function y = f(x) are given below. According to…

A: The graph of the first and second derivative of the function y = fx is The statement is f is…

Q: B. Find the value of x for which Inx + (Inx)2 + (Inx)+ (Inx)* + = 9

Q: Use this definition with right endpoints to find an expression for the area under the graph of f as…

Q: Determine the value of lim,00 7²+5 a +3r+7

Q: Given: cosg=-1, sin x =- 13 ,A is in the third quadrant, and x is in the fourth quadrant; evaluate…

A: This question is based on Trigonometric equation.

Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x2 + ax + B with…

Q: How to compare two numbers using binomial theorem. Explain step by step

A: Binomial theorem is a very powerful mathematical tool when it comes to comparing complicated…

Q: Differentiate y = (9x- 11) log3 (1læ – 9). %3D A. y' = 9(11x-9)+11(9z-11) In(9r-11) (9x-11) In(3)…

Q: find the derivative of y=4x^2+4x+1

Q: Which of the following statements is true for the function f whose derivative is f'(x) = (x + 2)e-*…

A: Here we have to find the intervals where the function is increasing and decreasing.

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t) e) (5cos2x-3tanx) /cosx

Q: The answer seem to be incorrect. By the way, this is a calculus question and not physics. The…

Q: 6. s) Rewrite (without any justification) the integral as an equivalent iterated integral in the…

Q: of limx¬∞ 6x²+5 x²+3x+7

Q: I do not understand the process. The process here shows alot of 0ddxx's I am unsure if this is an…

Q: The series 7 n3+ 9 n=1 6 n+ 1 is divergent. Select one: O True O False

A: Given query is to find that statement is true or false.

Q: Calculate the value of (1 + 2i)² and then use this value to find the roots of z – z + (1 – i) = 0.…

Q: Solve the differential equation below using series methods. y'' – 4xy' – y = 0, y(0) = 4, y'(0) = 2…

Q: solution

Q: Find the derivatiives of the following functions using DELTA METHOD. 1. f(x) = 3x – 2 2. f(x) = (3x…

A: We know that f'(x) = lim∆x→0fx+∆x - fx∆x

Q: Step 1 Given :x+ y = e2x + 2y -> Step 2 X + y = = e2x +2y di f ferenciate wrt x thenl - %3D

A: Let's find.

Q: Vectors a and b have lengths 2. If Ja + b | = V7, determine the exact value of Ja – b|.

Q: Express the circle specified by x = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A: Given:x=2cosθ and y=1+2 sinθWe need to express the circle in cartesian coordinates.

Q: f(x)=(5+x4)1/4 what is f2(x)

A: Given query is to find the second derivative of the expression.

Q: Find T(t) and N(t) at the given point. r(t) = (t – 2)i + tj; t = 2 4 i+j T(2) : V5 N(2) = i

Q: 5+5 =64x-1

Q: Suppose a firm's technology is represented by the production function f(L, K) = min(L, 2K), where L…

A: As we know that all isoquant curves are strictly negative sloped hence, if one of the point is (4,…

Q: Hi! I am a bit confused before the third step. How did you go from xsin-1y to 1-ln(xy)? Can you…

A: Given

Question

Bacteria are reproducing in concentric rings in a petri dish. The circular area occupied by the bacteria
is increasing at a rate of 4 cm^2/day. Find the rate of change of the radius of the circular area when the
radius is 5 cm. (A = πr^2)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Can the average rate of change of a function be constant?
A 12 m ladder is placed against a large building. The base of the ladder is resting on some slick ice, and it slips at the rate of 0.8 meter per minute. Find the rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 10 meters from the base of the building please explain
A \[10\]-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at \[3\] meters per minute. At a certain instant, the bottom of the ladder is \[6\] meters from the wall. What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
An ice cube in a freezer is growing due to accretion, each edge is increasing by 0.2 cm per minute. Find the rate at which the surface area is changing when the length of one side is 8cm.
The sides of an equilateral triangle extend at a rate of two cm per second. I drew a half-circle inside this triangle that touches two of its sides and began to expand with it. Find the rate of change of the area between the triangle and the half-circle when the length of the side of the triangle is 16 cm
The volume of a sphere is changing at a constant rate. Show that the surface area changes at a rate which varies inversely as the radius.
A 10 meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 3 meters per minute. At certain instant, the bottom of the leader is 6 meters from the wall. What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm /min. At what rate is the plate’s area increasing when the radius is 50 cm?
A spherical snowball is melting so that its diameter is decreasing at a rate of 0.4 cm/min. At what is the rate is the volume of the snowball changing when the diameter is 14 cm? The volume is changing at a rate of cm^3/min.
determine the instantaneous rate of change in: a. surface area of spherical balloon (as it inflated) at the point in time when the radius reaches 10 cm b. the volume of the spherical balloon (as it is deflated) at the point in time when the radius reaches 5 cm
When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.04 cm/min. At what rate is the plate's area increasing when the radius is 56 cm?
When a circular plate of metal is heated in a oven, its radius increases at a rate of 0.05 cm/min. at what rate is the plate's area increasing when the radius is 52cm?