An exponential decay model multiplies the remaining amount by a fixed factor each time the input rises by . If a scatterplot labels points on the model curve, use those coordinates rather than nearby data dots. Count the input steps, relate the outputs with a power of the factor, and use a Desmos regression to find the factor. The full output ratio isn't necessarily the one-step factor.
Hints
- Hint 1
The labeled points are on the model curve, so use their coordinates instead of estimating from the scattered measurements. Count the one-hour steps between their time coordinates before comparing the masses.
- Hint 2
In , the base multiplies the mass once per hour. The labeled times are three hours apart, so the later mass equals the earlier mass times . What equation does that give?
- Hint 3
To find the unknown factor in Desmos, put in place of and in place of . Desmos reports the fitted value under PARAMETERS.
Step-by-step
Find the one-hour factor from the labeled points
Step 1Count the hours between model points
Read the labeled points on the curve, and , rather than estimating from the scattered measurements. Their time coordinates differ by hours.
- Step 2
Turn the three-hour change into an equation
In , the base multiplies the mass once per hour. Starting at grams and moving ahead three hours, three hourly steps use , not . Write the later mass as: .
- Step 3
Find the factor in Desmos
Type . Here stands for , and tells Desmos to fit the unknown. Under PARAMETERS, Desmos shows . So the model multiplies the mass by about each hour. Choice C.