The following table shows the approximate average household income in the United States in 1990, 1995, and 2003. (t=0 represents 1990.) begin{array}{|c|c|}hline text{t(Year)} & 0 & 5 & 13 hline text{H(Household Income in} $1,000) & 30 & 35 & 43 hline end{array} Which of the following kinds of models would best fit the given data? Explain your choice of model. ( a, b, c, and m are constants.) a) Linear: H(t)=mb + b b) Quadratic: H(t)=at^{2} + bt + c c) Exponential: H(t)=Ab^{t}

Question
Exponential models
asked 2020-12-24
The following table shows the approximate average household income in the United States in 1990, 1995, and 2003. (\(\displaystyle{t}={0}\) represents 1990.)
\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{t(Year)}&{0}&{5}&{13}\backslash{h}{l}\in{e}\text{H(Household Income in}\ \${1},{000}{)}&{30}&{35}&{43}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
Which of the following kinds of models would best fit the given data?
Explain your choice of model. ( a, b, c, and m are constants.)
a) Linear: \(\displaystyle{H}{\left({t}\right)}={m}{b}\ +\ {b}\)
b) Quadratic: \(\displaystyle{H}{\left({t}\right)}={a}{t}^{{{2}}}\ +\ {b}{t}\ +\ {c}\)
c) Exponential: \(\displaystyle{H}{\left({t}\right)}={A}{b}^{{{t}}}\)

Answers (1)

2020-12-25
Step 1
Plot the points on acoordinate system.
Scetching the various models and their characteristics (see below), we find that the linear model would be best for this data set.
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Step 2
not exponential, because the rate of rising does not seem to change.
Not quadratic, because there are no "dips" or "bulges" to account for minimum/maximum values.
0

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