Question

The R-value of insulation is a measure of its ability to resist heat transfer. For fiber-glass insulation, 3½ inches is rated at R-11 and 6 inches is rated at R-19. Assuming this relationship is linear, write the equation that gives the R-value of fiberglass insulation as a function of its thickness t (in inches).
R =

Answer 1

Answer:

$R = \dfrac{16}{5}t + \dfrac{1}{5}$

where R is the R-value and t is the thickness in inches.

Step-by-step explanation:

We are given the following in the question:

The  R-value of fiberglass insulation and f its thickness have a linear relation.

Let R be the R-value and t be the thickness. Then, the equation can be written as:

$R = at + b$

where a and b are constants.

When t = 3.5, R = 11

$11 = 3.5a + b$

When t = 6, R = 19

$19 = 6a + b$

Solving the two equation, using the elimination method, we have,

$19-11 = 6a + b-(3.5a + b)\\8 = 2.5a\\\\\Rightarrow a = \dfrac{16}{5}\\\\11 = 6(\dfrac{16}{5}) + b\\\\\Rightarrow b = \dfrac{1}{5}$

Thus, the linear relationship is given by:

$R = \dfrac{16}{5}t + \dfrac{1}{5}$

where R is the R-value and t is the thickness in inches.