5.14.1 Distinguish Linear and Exponential Growth

Compare your answer:

All answers are acceptable if backed up by a reasonable explanation. Compare your answer:

• The graph is for $y=120+3.7x$ because it appears linear. On the graph, when $x=7$, the value of $y$ appears to be a little less than 150. When $x=7$, $120+(3.7)·7=145.9$, so the slope of the line could be 3.7.
• The graph is for $y=120·(1.03{)}^x$. Multiplying 100 by 1.03 seven times, or $100·(1.03{)}^7$, gives approximately 147.6, which more or less concurs with what is on the graph.
• It is hard to tell. I tried finding the $y$-coordinate values for different values of $x$ using both equations, and they more or less agree with what is on the graph.

Compare your answer:

Your answers may vary, but here are some examples:

• Exact coordinates of points on the graph with whole-number $x$-values
• A larger graphing window showing larger domain values so that the behavior of the function can be more visible