Algebra 1
Exponential functions
Comparing linear and exponential models
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Questions
Question 1
168143
The two tables below show values of two different functions. \[ \textbf{Table A} \begin{array}{|c|c|} \hline x & y
\hline 0 & 3
1 & 7
2 & 11
3 & 15
\hline \end{array} \qquad \textbf{Table B} \begin{array}{|c|c|} \hline x & y
\hline 0 & 3
1 & 6
2 & 12
3 & 24
\hline \end{array} \] Classify each table as linear or exponential. Justify your answer using differences or ratios.
Table A — differences: 7-3=4, 11-7=4, 15-11=4. Constant differences → LINEAR. Equation: y=4x+3. Table B — ratios: 6/3=2, 12/6=2, 24/12=2. Constant ratios → EXPONENTIAL. Equation: y=3·2^x. Key rule: constant differences = linear; constant ratios = exponential.
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