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?

Question

[(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

Answer 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