Question

aEvery year since 1548, the average height of a human male has increased slightly. Thenew height is 100.05% of what it was the previous year. If the average male's height was54 inches in 1548, what was the average height of a male in 2008?

Answer 1

Given:

a.) The new height is 100.05% of what it was the previous year.

b.) The average male's height was 54 inches in 1548.

For us to be able to determine the average height of a male in 2008, we will be using the geometric sequence formula:

`A_n\text{ = }A_1(r)^(n-1)`

Where,

An = The average height of a male in 2008

A1 = 54 inches

r = 100.05% = 100.05/100 = 1.0005

n = (2008 - 1548) + 1 = 460 + 1 = 461

We get,

`A_n\text{ = }A_1(r)^(n-1)`
`A_n\text{ = }(54)(1.0005)^(461-1)\text{ = }(54)(1.0005)^(460)`
`=(54)(1.2585276666222281763001496826748)`
`=\text{ }67.960493997600321520208082864439`
`\text{ }\approx\text{ 67. 96 inches}`

Therefore, in 2008, the average height of a male will be 67.96 inches.