The base-10 log table shows that the value of \(\log_{10} 50\) is about 1.6990. Explain or show why it makes sense that the value is between 1 and 2.

What is the value of \(\log_{10}(1,\!000,\!000,\!000)\)? Explain how you know.

A bank account balance, in dollars, is modeled by the equation \(f(t) = 1,\!000 \boldcdot (1.08)^t\), where \(t\) is time measured in years.

About how many years will it take for the account balance to double? Explain or show how you know.

The graph shows the number of milligrams of a chemical in a test tube, \(d\) days after it was first measured.

1. Explain what the point \((1,2.5)\) means in this situation.
2. Mark the point that represents the amount of the chemical left in the test tube after 8 hours.

The exponential function \(f\) takes the value 10 when \(x = 1\) and the value \(30\) when \(x = 2\). 

1. What is the \(y\)-intercept of \(f\)? Explain how you know.
2. What is an equation defining \(f\)?