Question

Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = 2x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.

Answer 1

The logarithmic model for the length when the strength is of 8 Pascals is given by:

• $f^{-1}(8) = \log_{2}{8} = \log_2{2^3} = 3$
• That is, the length is of 3 units.

What is the function?

The strength in Pascals for a building of length x is given by:

$f(x) = 2^x$

To find the length given the strength, we apply the inverse function, that is:

$2^y = x$

$\log_{2}{2^y} = \log_2{x}$

$y = \log_2{x}$

Hence, when the strength is of 8 Pascals, $x = 8$, and the length is given by:

$f^{-1}(8) = \log_{2}{8} = \log_2{2^3} = 3$

You can learn more about logarithmic functions at brainly.com/question/25537936