Exercises: Fit a Function to Data

A regression on real data produces the equation $y = 2.1x + 15$, and it tracks the scatter plot's trend closely. Which statement best describes what this fitted function is?

Which function family produces a graph that rises to a turning point and then falls (a U-shape or upside-down U)?

A context supplies the linear function $y = 0.10x + 20$ for the monthly cost $y$ (in dollars) of a phone plan after $x$ minutes of calls. Evaluate the function at $x = 200$ minutes. Give the cost in dollars.

The scatter plot below shows data that increases by roughly the same amount for each equal step in $x$ — the points fall close to a straight line. Which model family best fits this data?

The scatter plot below shows a ball's height versus time after a throw: the points rise to a peak and then fall back down. Which model family best fits this data?

The scatter plot below shows a bacteria count versus hours: the points stay low at first, then curve steeply upward, roughly multiplying each hour. Which model family best fits this data?

A bacteria population is modeled by the exponential function $y = 50 \cdot 2^{x}$, where $x$ is the number of hours and $y$ is the count. Predict the count after $x = 3$ hours.

Using the fitted phone-plan function $y = 0.10x + 20$ (cost $y$ in dollars for $x$ minutes), how many minutes $x$ give a bill of $y = 35$ dollars? Solve for $x$.