Question

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)

Answer 1

Answer:

$g(f(d)) = -dlog_{10}(0.5 * 10^{-4})$

Step-by-step explanation:

Given

$f(d) = (0.5 * 10^{-4})^d$

$g(H+) = -log_{10}(H+)$

Required

Find the composite function g(f(d))

We have:

$g(H+) = -log_{10}(H+)$

Substitute f(d) for H+

$g(f(d)) = -log_{10}(f(d))$

Substitute $f(d) = (0.5 * 10^{-4})^d$

$g(f(d)) = -log_{10}((0.5 * 10^{-4})^d)$

Apply law of logarithm

$g(f(d)) = -dlog_{10}(0.5 * 10^{-4})$

Hence, the function is:

$g(f(d)) = -dlog_{10}(0.5 * 10^{-4})$

Answer 2

Answer:

It's C

Step-by-step explanation: