Question

The dissolve (decay) rate of 200 mg of medication in the bloodstream of a patient is shown in the table, where y is the amount of medicine (in mg), and x is hours.

Use the table to answer the question.

Hours x 0 1 3 5
Amount (mg) y



0 160 102 66
What is the rate of decay for the interval 1–3 hours?(1 point)
The rate of decay for the interval 1–3 hours is
mg/hour.

Answer 1

To calculate the rate of decay for the interval from 1 to 3 hours, we need to find the amount of medication at these two time points and then calculate the difference in amount over the time interval.

From the table:
- At \( x = 1 \) hour, \( y = 160 \) mg
- At \( x = 3 \) hours, \( y = 102 \) mg

1. **Calculate the change in amount:**
\[
\text{Change in amount} = y(3) - y(1) = 102 \, \text{mg} - 160 \, \text{mg} = -58 \, \text{mg}
\]

2. **Calculate the change in time:**
\[
\text{Change in time} = 3 \, \text{hours} - 1 \, \text{hour} = 2 \, \text{hours}
\]

3. **Calculate the rate of decay:**
\[
\text{Rate of decay} = \frac{\text{Change in amount}}{\text{Change in time}} = \frac{-58 \, \text{mg}}{2 \, \text{hours}} = -29 \, \text{mg/hour}
\]

The rate of decay for the interval 1–3 hours is \(-29 \, \text{mg/hour}\).