Question

amount of hydrogen vs. ph
amount of hydrogen, x (in moles per liter) ph, f(x)
$\frac{1}{10}$ 1
$\frac{1}{100}$ 2
$\frac{1}{1,000}$ 3
$\frac{1}{10,000}$ 4
$\frac{1}{100,000}$ 5
which function models the data in the table?

Explanation:

Step1: Recall the pH formula

The formula for pH is $f(x)=-\log_{10}(x)$, where $x$ is the amount of hydrogen in moles per liter.

Step2: Test values from the table

For $x = \frac{1}{10}$, $f(x)=-\log_{10}(\frac{1}{10})=-\log_{10}(10^{- 1})=-(-1)=1$.
For $x=\frac{1}{100}$, $f(x)=-\log_{10}(\frac{1}{100})=-\log_{10}(10^{-2})=-(-2) = 2$.
For $x=\frac{1}{1000}$, $f(x)=-\log_{10}(\frac{1}{1000})=-\log_{10}(10^{-3})=-(-3)=3$.
For $x = \frac{1}{10000}$, $f(x)=-\log_{10}(\frac{1}{10000})=-\log_{10}(10^{-4})=-(-4)=4$.
For $x=\frac{1}{100000}$, $f(x)=-\log_{10}(\frac{1}{100000})=-\log_{10}(10^{-5})=-(-5)=5$.

Answer:

The function $f(x)=-\log_{10}(x)$ models the data in the table.