The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 5% in 10 years. What will be the population in 50 years? How fast is the population growing at  t = 50?  show all work

Q: dy 7. a) Prove that, fo-y4 = 4√/2n e2x b) Prove that, √∞ (e³x+1)² dx: = 2π 9√3

A:

Q: What is the component form of a vector with a magnitude of 17 and a direction of 125°? Show how to…

A:

Q: O Country A had a GDP per capita of $10000 and Country B had a GDP of 1000 in 1960. Country A has…

A:

Q: 8. Determine the equation of the tangent line to the curve y = -x² − 3x + 4 at x = 2.

A:

Q: Consider A ABC, where a = 8, c = 11, and m/C = 33°. What are the measures of the missing angles and…

A:

Q: 1. Differentiate. a) f(x) = x43x b) g(x) = x² — e√x -

A: We need to perform differentiation.

Q: 2 Determine and classify the critical point(s) for the function g(x) = x²(x − 3)²³.

A:

Q: Show that there are no points on the graph where tanx is horizontal.

A:

Q: Given the Pythagorean theorem a² + b² = c² where a and b are the lengths of the perpendicular sides…

A:

Q: 15 years ago, a company started depositing money into an investment account earning interest at an…

A:

Q: 2. Differentiate a) each of the following functions. Leave in unsimplified form. b) f(x) =…

A: 2)a) y=x6+5 sqrt(x)b) f(x)=3sinx - cos4xDifferenciate the given functions.

Q: (b) Consider the first order linear differential equation dy Y + dx x-1 = 2 (i) Find the integrating…

A: Consider the first order linear differential equation.(i) To find the integrating factor for this…

Q: If the rate of change of Q is inversely proportional to Q where Q > 0. If Q(0) = 250, and Q(2) =…

A: Given problem:-If the rate of change of Q is inversely proportional to Q where Q > 0. If Q(0) =…

Q: Use the graph to determine the domain a -16 -12 -8 X=-3 16- ¹12- 8- 12- y = 5 8 i x = 3 12 X 16

A: The graph of the function isTo determine: The domain and the range of the function.

Q: Jane is taking a history class. The teacher states that the population of a country is shrinking at…

A: Size of the population, P = 10e0.5t

Q: What is the domain of g(x,y)= 12 xy Select the correct choice below and fill in any answer boxes…

A: Given We need to find the domain of the function.

Q: The family of curves represented on this graph would appear to be consistent with which of the…

A: Y

Q: Find equations for the tangent plane and the normal line at point Po (Xo Yo-Zo) (2,3,0) on the…

A:

Q: q 22. 16 determine the magnitude and direction of the vector v = and also show that  v = |v|u ,…

A:

Q: 1. Complete the following analysis for the function f(x) = = Note that the first and second…

A:

Q: Determine the following product. [2 -2 5 2] 3 H = [ 1 ]

A:

Q: Factor the following expression by grouping.   x3−2x2+3x−6

A: let

Q: 4. Find the local extrema for the given function below. No graphs. f(x) = x + ln(x² + 1)

A:

Q: Find the magnitude and direction angle for each vector. • 431-46j (5.-6) 6) RS where R=(3,-1) S=

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: 3. Determine vector and parametric equations of the plane with Cartesian equation 3x - 2y +z + 6 =…

A: Cartesian equation of plane is

Q: Use the chain rule to find z = sin(8) dz дz and əs at r = st, 8 = s³ + ³

A:

Q: Evaluate the double integral 11₁₂²² x² dA, where D = {(x, y) : 1 ≤ x ≤e,0 ≤ y ≤ lnx}.

A:

Q: Multiply. cis (3)cis (2)

A:

Q: O O y=3x² + C y = Ce ¹/2x2 – 1 = 1/2 e*² y=C√x+3 y= +C

A:

Q: Use the limit definition of partial derivatives to compute the partial derivative of the function…

A:

Q: Suppose the rate at which the volume in a tank decreases is proportional to the square root of the…

A:

Q: Suppose the rate at which the volume in a tank decreases is proportional to the square root of the…

A:

Q: Find all the second-order partial derivatives of the following function. w=5ye3x² - 4y

A: w= 5ye3x^2-4yWr have to find all second order partial derivatives

Q: For the functions w = 2x² + 3y², x= cost, and y = sint, express terms of t and differentiating…

A:

Q: M 12 M Let p(x) = x³ – 5x² + 4x − 20. Verify that p(5) the other roots of p(x) = 0 over the complex…

A:

Q: Suppose F(x) = f(x³), G(x) = (ƒ(x)) and: a² = 11, f(a)=2, f'(a)=14, ƒ'(a³) = 8. Find: (a) F'(a) =…

A: given given

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4. 2 #…

A:

Q: Use the pair of functions f(x): = x² + 5, f(g(x)) = g(f(x)) = to find (g(x)) and g(f(x)). Simplify…

A: given

Q: For what value of the number k is the following function continuous at r=2 if x 2 f(x) = = (A) 3…

A:

Q: Discover all unit vectors that have an angle of T/3 with the positive section of the x-axis.

A:

Q: According to the properties of logarithms log(8) = 3log(2) O True False

A:

Q: tan (sin ¹(-)) cos (tan ¹(1)) Enter your answer, as a simplified fraction, in the box. What is the…

A: let

Q: Write the following in exponential form: y = In(0.34) O 3.4⁰ = y O e = 0.34 O e³.4 = y O 3.4 = e

A: The given equation is; y=ln(0.34)Write in exponential form.

Q: Find Vf at the given point. f(x,y,z)=x² + y² - 3z²+z Inx. (1,4,3) Vf|(1,4,3)+(+(k (Simplify your…

A: Given:We are required to find:

Q: 1. у ул y=3x - x² 0 y=x (2, 2) AX

A:

Q: 6. Find the limit or explain why it does not exist (and if it is too). √16x4+7x 8x² +5 (i) lim 818

A:

Q: O с 5. Given the function below, what would be the domain of the function's inverse? 1/2 -0.5 ≤x≤0.5…

A: Domain of a function f(x) is defined as the set of valued of x for which the function gives a…

Q: Rewrite the following equation with the variables separated. y' = 6xy² + 2xy + 6y² + 2y

A:

Q: find exact value using diagram of four quadrants. please draw the diagram. 1) 2sin 2) cos² sin² 6 3)…

A:

Q: Find the Jacobian for a u²+ 8uv and y = 6uv². Jacobian (equation format) Submit Question

A: