Math

Suppose a tree on your land has a radius of 3 inches and increases in radius one-fourth inch a year. How many years, y, to the nearest tenth will it take for the volume of the tree to double? In other words, for what value of y would the following be true?

[(1/3)πk(3 + ¼ y)^8/3] = 2[(1/3)πk(3)^8/3]

a. 6.1 years
b. 6.2 years
c. 3.6 years
d. 2.0 years

  1. 👍
  2. 👎
  3. 👁
  1. you can factor out the πk/3 and solve
    (3 + ¼ y)^8/3 = 2(3)^8/3
    3 + ¼ y = 2^3/8 * 3
    ¼ y = 3(2^3/8 - 1)
    y = 12(2^3/8 - 1) = 3.56207

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    volume of cone varies jointly as square of its radius and its height if volume of a cone is 27pie cubic inches when radius is 3 inches and height is 9 inches find volume of a cone when radius is 4 inches and height is 3 inches

  2. calculus

    A candy company needs a custom box for their truffles. The box they've chose is in the shape of a cylinder with a hemisphere of the same radius on top. The total volume of the box is V= (1/2) ((4pir^2)/(3))+ pir^2 (y-r), where y

  3. calculus

    1. The radius of a sphere is r inches at time t seconds. Find the radius when the rates of increase of the surface area and the radius are numerically equal. A 1/4π in B 1/5π in C 1/3π in D 1/8π in E 1/2π in

  4. calculus

    A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is

  1. calculus

    sand is being dropped onto a conical pile in such a way that the height of the pile is always twice the base radius.what is the rate of change of the volume of the pile with respect to the radius when the radius of the pile is 12

  2. Chemistry

    Which trends are observed when the elements in Period 3 on the Periodic Table are considered in order of increasing atomic number? (1) The atomic radius decreases, and the first ionization energy generally increases. (2) The

  3. calculus

    At the instant when the radius of a cone is 3 inches, the volume of the cone is increasing at the rate of 28.27433388 cubic inches per minute. If the height is always 3 times the radius, find the rate of change of the radius at

  4. algebra

    The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 50π cubic inches when the radius is 5 inches and the height is 6 inches, find the volume of a cone when the radius is 4

  1. AP calculus AB

    At the instant when the radius of a cone is 3 inches, the volume of the cone is increasing at the rate of 9 pi cubic inches per minute. If the height is always 3 times the radius, find the rate of change of the radius at that

  2. Math

    For any circle, which ratio is equal to the number π? Select all that apply. ***A. Circumference ------------------- Diameter B. Circumference ------------------- Radius ***C. Circumference ------------------- 2 Times Radius D.

  3. math

    a rectangular container with dimensions 10 inches by 15 inches by 20 inches is to be filled with water, using a cylindrical cup whose radius is 2 inches and whose height is 5 inches, what is the maximum number of full cups of

  4. calculus

    Water leaking onto a floor creates a circular pool with an area that increases at the rate of 3 square inches per minute. How fast is the radius of the pool increasing when the radius is 10 inches?

You can view more similar questions or ask a new question.