Technology required. Function \(f\) is defined by \(f(x) = 3x + 5\), and function \(g\) is defined by \(g(x) = (1.1)^x\).

Functions \(m\) and \(n\) are given by \(m(x)=(1.05)^x\) and \(n(x)=\frac58 x\). As \(x\) increases from 0:

1. Which function reaches 30 first?
2. Which function reaches 100 first?

The functions \(f\) and \(g\) are defined by \(f(x) = 8x + 33\) and \(g(x) = 2 \boldcdot (1.2)^x\).

1. Which function eventually grows faster, \(f\) or \(g\)? Explain how you know.
2. Explain why the graphs of \(f\) and \(g\) meet for a positive value of \(x\).

A line segment of length \(\ell\) is scaled by a factor of 1.5 to produce a segment with length \(m\). The new segment is then scaled by a factor of 1.5 to give a segment of length \(n\).

What scale factor takes the segment of length \(\ell\) to the segment of length \(n\)? Explain your reasoning.

A couple needs to get a loan of \$5,000 and has to choose between three options.

• Option A: \(2\frac{1}{4}\%\) applied quarterly
• Option B: \(3\%\) applied every 4 months
• Option C: \(4\frac{1}{2}\%\) applied semi-annually

If they make no payments for 5 years, which option will give them the least amount owed after 5 years? Use a mathematical model for each option to explain your choice.

Here are graphs of five absolute value functions. Match the graph and equation that represent the same function.