Chemists use pH as a measure of acidity or alkalinity of a solution. It uses the concentration of hydrogen ions H+ in a logarithmic function. A chemist is studying the alkalinity of a hot spring near a volcano. The hydrogen ion concentration is increasing according to the function f(d) = (0.5 × 10–4)d, where d is the number of days. The function for pH is g(H+) = –log10(H+), where H+ is the hydrogen ion concentration of the solution. Which function shows the pH of the hot spring as a function of d? g(f(d)) = –log10(d) g(f(d)) = –d(log10(0.5 × 10–4)) g(f(d)) = –log10((0.5 × 10–4)d) g(f(d)) = –log10(d × 10–4)

Respuesta :

Answer:

[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]

Step-by-step explanation:

Given

[tex]f(d) = (0.5 * 10^{-4})^d[/tex]

[tex]g(H+) = -log_{10}(H+)[/tex]

Required

Find the composite function g(f(d))

We have:

[tex]g(H+) = -log_{10}(H+)[/tex]

Substitute f(d) for H+

[tex]g(f(d)) = -log_{10}(f(d))[/tex]

Substitute [tex]f(d) = (0.5 * 10^{-4})^d[/tex]

[tex]g(f(d)) = -log_{10}((0.5 * 10^{-4})^d)[/tex]

Apply law of logarithm

[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]

Hence, the function is:

[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]

Answer:

It's C

Step-by-step explanation: