The density of atmosphere (measured in kilograms/meter3) on a certain planet is found to decrease as altitude increases (as measured from the planet's surface). what is the type of relationship between the height (h) and the atmospheric density, and which segment can give the most accurate approximations for the interpolated values?

see the attached figure to better understand the problem

we know that

A relationship between two variables, D and H, represent an inverse variation if it can be expressed in the form

where

D---------> is the atmospheric density in

H------> is the altitude in km

k -----is a constant

if the atmospheric density increase, then the altitude decrease and if the atmospheric density decrease, then the altitude increase

The segment that can give the most accurate approximations is the CD segment, since it is the CD interval that is closest to a straight line.

therefore

the answer is

The type of relationship between the height (H) and the atmospheric density is an inverse variation and the most accurate approximations for the interpolated values is the segment CD

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.