Labeled points on an exponential model give you a multiplier for the gap between their inputs. Divide the later model output by the earlier one, then raise that multiplier to the requested interval divided by the gap. Use points on the curve, not nearby measured dots, and don't mistake a multiweek multiplier for a one-week multiplier.
Hints
- Hint 1
The model curve gives predicted counts; the gray circles show measurements that may miss the curve. Which two labeled markers lie exactly on the model, and how many weeks separate them?
- Hint 2
A multiplier is the later predicted count divided by the earlier one. That ratio applies over the time between the two markers, not automatically over one week.
- Hint 3
An exponent counts how many times a multiplier applies. Divide the requested time gap by the gap between the marked points. What power of the marked points' multiplier does that give?
Step-by-step
Use the multiplier between model points
Step 1Read the model points and their time gap
The black diamonds at and lie on the model curve, so its predicted count goes from to over weeks. Don't use a nearby gray circle: it shows a measurement, not the model's prediction.
- Step 2
Find the four-week multiplier
A multiplier is the later count divided by the earlier count. Type in Desmos. It shows ; tap the fraction button to see . So the model multiplies the count by over 4 weeks.
- Step 3
Convert the multiplier to six weeks
In , a -week increase adds to the exponent, so the multiplier you found is . A -week increase multiplies by . Express that power using the known four-week multiplier:
- Step 4
Evaluate the six-week factor
Keep the first Desmos line and type . Desmos shows ; the fraction button gives . So after 6 more weeks, the predicted bacteria count is multiplied by . Choice B.