Question

1. a new medication is being studied to see how quickly it is metabolized in the body. starting with an initial dose of 15 milligrams in the bloodstream, it declined to 10.7 milligrams after 5 hours. complete the table to determine which of these equations could approximate the amount of milligrams. equation: yes no m = 10.7(0.71)^n m = 10.7(0.93)^n m = 15(0.93)^n m = 15(0.71)^n 2. the data gives the estimated value in dollars of a model of a classic car over several years. 15,300 16,100 17,300 18,400 19,600 20,700 22,000 find an approximate exponential model for the cars value by averaging the successive ratios of the value. you can solve by using a scientific calculator or use the exponential regression tool.

Explanation:

Step1: Identify the formula for medicine problem

Use \(m = 15(0.93)^{n}\), \(n = 5\) for 5 - hour time period.

Step2: Calculate \((0.93)^{5}\)

\((0.93)^{5}=0.6956887849\)

Step3: Multiply by initial amount

\(m = 15\times0.6956887849\approx10.4\)

Answer:

1.
For the medicine - related problem:
We need to use the formula \(m = 15(0.93)^{n}\) (assuming \(n = 5\) for 5 hours).

$$m=15\times(0.93)^{5}$$

$$m = 15\times0.6956887849$$

$$m\approx10.43533177\approx10.4$$

milligrams

For the car - value problem:
We are not given a specific \(n\) (number of years) to find the value. But if we assume we want to find the general form of the exponential decay model for the car's value, and we know the general form of an exponential decay model is \(y = a(1 - r)^{n}\), where \(a\) is the initial value and \(r\) is the rate of decay. Here we would need more information like the initial value of the car and the rate of decay per year to calculate a specific value.