A fixed percent change each hour signals exponential change: the same fraction of the current amount is used again and again. Find the fraction that remains after one hour, then check whether repeated multiplication makes the amount grow or shrink. A decrease alone doesn't mean a line with a negative slope; a line loses the same number each hour.
Hints
- Hint 1
A percent decrease gives the part removed, not the part left. Start with of the bacteria present at the beginning of an hour. What percent remains at the end of that hour?
- Hint 2
A linear model loses the same number each hour. If the loss is a percent of the bacteria currently present, does each hour subtract a fixed number or multiply by a fixed factor?
Step-by-step
Track the fraction remaining
Step 1Find the hourly multiplier
No Desmos needed. The wording gives the change rule directly. A decrease leaves part of the current count behind. Find the percent left:
Write that percent as a multiplier, the number applied to the current count:
- Step 2
Apply the multiplier repeatedly
Let be the count when the antibiotic is added, and let be the count after hours. Each hour starts with the previous hour's count, so multiply by again for each hour:
Each percent loss acts on the amount left after the previous loss.
- Step 3
Name the model
In , time is in the exponent because the multiplier repeats. That's an exponential model. Since is between and , the number of bacteria shrinks over time. The number remaining follows an exponential decay model. Choice D.
Lessons that teach this
- SAT Nonlinear FunctionsIntermediateCoreBuild, identify, and interpret exponential models
- SAT Data AnalysisIntermediateModel percent increase and decrease
- SAT AlgebraBeginnerBuild and use linear models
- DesmosAdvancedCoreExponential models, transformations, and Log Mode
- DesmosIntermediateSolve percent problems in Desmos