[size=150]List them in order of increasing rate of change. That is, start with the one that grows the slowest and end with the one that grows the quickest.[br][br][table][tr][td][math]a(x)=5x+3[/math][/td][td][math]b(x)=3x+5[/math][/td][td][math]c(x)=x+4[/math][/td][td][math]d(x)=1+4x[/math][/td][/tr][/table][/size]
[size=150]Function [math]f[/math] is defined by [math]f\left(x\right)=3x+5[/math] and function [math]g[/math] is defined by [math]g\left(x\right)=\left(1.1\right)^x[/math][/size].[br]Complete the table below with values of [math]f\left(x\right)[/math] and [math]g\left(x\right)[/math]. When necessary, round to 2 decimal places. You may use the scientific calculator beneath the table to help with calculations.
Which function do you think grows faster? Explain your reasoning.
What graphing window do you have to use to see the value of [math]x[/math] where [math]g[/math] becomes greater than [math]f[/math] for that [math]x[/math]?
[size=150]Functions [math]m[/math] and [math]n[/math] are given by [math]m\left(x\right)=\left(1.05\right)^x[/math] and [math]n\left(x\right)=\frac{5}{8}x[/math]. As [math]x[/math] increases from 0:[/size][br]Which function reaches 30 first?[br]
Which function reaches 100 first?[br]
[size=150]The functions [math]f[/math] and [math]g[/math] are defined by [math]f\left(x\right)=8x+33[/math] and [math]g\left(x\right)=2\cdot\left(1.2\right)^x[/math].[br][/size][br][size=100]Which function eventually grows faster, [math]f[/math] or [math]g[/math]? Explain how you know.[/size]
Explain why the graphs of [math]f[/math] and [math]g[/math] meet for a positive value of [math]x[/math].[br]
[size=150]A line segment of length [math]\ell[/math] is scaled by a factor of 1.5 to produce a segment with length [math]m[/math]. The new segment is then scaled by a factor of 1.5 to give a segment of length [math]n[/math].[/size][br][br]What scale factor takes the segment of length [math]\ell[/math] to the segment of length [math]n[/math]? Explain your reasoning.
[list][*]Option A: [math]2\frac{1}{4}\%[/math] applied quarterly[/*][*]Option B: [math]3\%[/math] applied every 4 months[/*][*]Option C: [math]4\frac{1}{2}\%[/math] applied semi-annually[/*][/list]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.