A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 480. (a) Find an expression for the number of bacteria aftert hours. P(E) (b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.) P(4) = X bacteria (c) Find the rate of growth after 4 hours. (Round your answer to the nearest whole number.) P'(4) = x bacteria per hour (d) When will the population reach 10,000? (Round your answer to one decimal place.) X hr Enhanced Feedback Please try again. Recall that a bacteria culture with growth rate proportional to the size of the culture has a growth function in the form of P(t) = P(0)e*t, where P(0) is the initial value and k is the growth rate. Find k by replacing other values in the equation wi values from the problem. .......................... .... ..... -................................... ................

Q: Determine the function f satisfying both the conditions f'(=) = sec ( 5 ) tan (5) (4) tan (3) f(플) %...

A: Given: f'(x)=secx3 tanx3 ;           such that  fπ2=4

Q: What is the y-intercept of y = tanx?

A: y=tanx

Q: Calculate the rate of change of escape velocity vesc = (2.82 × 107)r −1/2 m/s with respect to distan...

A: Given, vesc=2.82×107r-12 m/s where r is a distance from the center of the earth.

Q: The number of bacteria in a culture is increasing according to the law of exponential growth. There ...

A:

Q: For the right triangles below, find the exact values of the side lengths b and a. If necessary, writ...

A: In a 30-60-90 triangle, the side opposite to 30 is half of the hypotenuse, and the side opposite to ...

Q: lity to determine how many terms of the Maclaurin ser |x| < 0.1 with error less than 0.0001.

A:

Q: What is the closure property of addition? (applied to matrices)

A: Closer property of addition  A+Bis a matrix of the same dimension as A and B Notice that the sum of ...

Q: use the shell method to find the volumes of the solids generated by revolving the shaded regions abo...

A: Solution:- The volume of the solid about the line y=5 The shell thickness is y and the limits of y v...

Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double i...

A: We have to find the value of area of region shaded.

Q: 3.2.6 Theorem If X (x) is a convergent sequence and if a S XnSb for all n eN, then a < lim(x,n) sb. ...

A: To prove: a≤limn→∞xn≤b Given information: The sequence X=xn is a convergent sequence and if a≤xn≤b.

Q: solve each inequality algebraically.

A: To solve: Inequality x+12x&lt;7. Calculation: Simplify the inequality as follows: x+12x&lt;7x2+12x&l...

Q: Differentiate  y = (ln x)5

A: Given that the function is  y = (ln x)5 To differentiate with respect to x

Q: Find k such that the line is tangent to the graph of the function.

A: The function is given as fx=kx......(1) The line is given as y=x+4......(2)  

Q: 2-9. Taylor polynomials Find the nth-order Taylor polynomial for the following functions centered at...

A: We have to write the Taylor polynomial which states                      (1)

Q: Problem 9

A:

Q: In Problems 1-3, for the given functions fand g. find: (a) (fog) (2) (b) (gof)(-2) (c) (fof) (4) 2. ...

A:

Q: A salesperson’s weekly pay depends on the volume of sales. If she sells x units of goods, her pay is...

A: Given straight line is  y=5x+60 Standard equation of  the straight line is  y=mx+c where, Slope=my-i...

Q: 3.2.6 Theorem If X (x) then a < lim(x) b. is a convergent sequence and if a S X5bfor all n e N,

A:

Q: thanks

A:

Q: lim 9 x^2-81/x-9 What would the factorization look like in the numerator?

A:

Q: Determine the area in the second quadrant enclosed by the equation y = 2x + 4 and the x- and y-axes.

A: Here we have to Determine the area in the second quadrant enclosed by the equation  y=2x+4 and the x...

Q: 19. Minimizing surface area. Mendoza Soup Company is constructing an open-top, square-based, rectang...

A: Given: Volume=32 ft3

Q: Find the area of the surface. The portion of the paraboloid  z = 49 − x2 − y2 in the first octant

A:

Q: Use the definite integral to find the area between the x-axis and ƒ(x)  over the indicated interval....

A: Consider the given function as fx=2-2x2

Q: Find all extreme values (if any) of f(x) = 3x²/3 + x on the interval 27 27 Determine at which number...

A:

Q: Every polynomial function of odd degree with real coefficients will have at least ................re...

A: To determineEvery polynomial function of odd degree with real coefficients willhave atleast 

Q: What are the possible angles θ between two unit vectors e and f if ||e × f|| = 1/2 ?

A: The cross product of two vectors can be found by the formula a→×b→=a→b→sinθ The magnitude of the cro...

Q: Use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum.

A: A geometric sequence is a sequence with a fixed ratio of consecutive terms. The ratio is called the ...

Q: Given the system of equations below, complete parts a, b, c, and d. F(x,y,z,u,v,w) = 11x- 3y – 6z² –...

A: According to question given that f(x,y,z,u,v,w)=11x-3y-6z2-3u+6v2-477=0G(x,y,z,u,v,w)=22x-6y+5z+5u2-...

Q: At what points are the functions continuous? x + 3 f(x) 2 - et

A: The given function is fx=x+32-ex

Q: Q4(^) calculus. Please explain every step, step by step, even small step, clearly using any definiti...

A:

Q: In the given equation, find the slope of the graph of the function at the given point. Use the deriv...

A: y=4x+12   at    0, 1

Q: find a general formula for f (n)(x). f (x) = x−1/2

A: The principle of Mathematical Induction is a technique that is used to determine the general formula...

Q: Exploring powers of sine and cosine a. Graph the functions fi(x) = sin? x and f2(x) = sin² 2r on the...

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want ...

Q: -2- 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx + 2. ANSWER: 4. USING THE DERIVATIVE IN ...

A:

Q: A new dot.com business began with an initial stock offering of $4,000. At the end of the first year,...

A:

Q: Problem 7

A:

Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The remainin...

A: First draw a picture and let the length of the bank of the river be l and then solve.

Q: 9. Mr. Solverson wants to spread mulch in a triangular region of his backyard that measures 10 fee b...

A: As the length of sides of the triangular region is 10ft, 14ft, and 21ft, we find the area A of the r...

Q: Problem 5

A:

Q: Suppose the functions f(x) and g(x) are defined for all x and that lim,0 f(x) = 1/2 and lim, o 8(x) ...

A: Given:            limx→\0f(x)=12  and limx→\0g(x)=2 

Q: Solve 2 sin (x) – 3 sin(x) + 1 = 0 for all solutions 0 < æ < 2n. -

A: Given,          2sin2x-3sinx+1=0

Q: use the integral test, evaluate your integral by hand with work shown.

A:

Q: Find an equation for the tangent line of e + 2xy = 2x – 1 at (1,0).

A: Topic- application of derivatives

Q: Evaluate the limit given limx→c f(x) = −6 and limx→c g(x) = 1 /2.

A: Given  limx→cf(x)=−6limx→cg(x)=12  

Q: Solve:(a) write the linear function f that has the given function values and (b) sketch the graph of...

A: (a) To find: The linear function fx . Given: The value of functions are f1=4 and f0=6. Calculation: ...

Q: 4. Eliminate the parameter and write the parametric equation in rectangular form x = 3 sece, y = 5 t...

A:

Q: True or false: To verify the identity sin x 1 + cos x we should begin by multiplying both sides by s...

A:

Q: Find the first four terms of the sequence defined by a, = 3 %3D а, 3 За, —1 + 2, for all n > 1

A: Put one by one n = 2, 3 ,4 in the given sequence and calculate first four terms.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.