Question

Ali drinks a beverage with 120 milligrams of caffeine. Each hour, the amount of caffeine in your system decreases by 12% each hour, the situation can be modeled using the equation. A is the amount of caffeine in your body after t hours. Identify the key features of the graph and interpret the meaning of the data.

As 1 increases, A (Dropdown 1: Increases, decreases) (Dropdown 2: Slowly, quickly) at first at then (Dropdown 3: Quickly, slowly)

The y-intercept is (Dropdown 4: Greater, lesser) than (Dropdown 5: 0, 120, 0.88)

The A-values are (Dropdown 6: greater, lesser) than (Dropdown 7: 0, 120, 0.88)

The amount of caffeine in the body continues to (Dropdown 8: Increase, decrease) over time

Answer 1

Filled dropdowns:
1. decreases
2. quickly
3. slowly
4. greater
5. 0
6. lesser
7. 120
8. decrease

Brief interpretation:
- The model is A(t) = 120(0.88)^t. At t = 0 the y-intercept is 120 mg (so it is greater than 0).
- As t increases, the caffeine amount decreases quickly at first and then more slowly, approaching 0 but never reaching it (A-values are less than 120 and remain positive).
- Therefore the amount of caffeine in the body continues to decrease over time.