Technology required. A function, \(f\), gives the number of stray cats in a town \(t\) years since the town started an animal control program. The program includes both sterilizing stray cats and finding homes to adopt them. An equation representing \(f\) is \(f(t) = 243 \left( \frac13 \right)^t\).

1. What is the value of \(f(t)\) when \(t\) is 0? Explain what this value means in this situation.
2. What is the approximate value of \(f(t)\) when \(t\) is \(\frac{1}{2}\)? Explain what this value means in this situation.
3. What does the number \(\frac13\) tell you about the stray cat population?
4. Use technology to graph \(f\) for values of \(t\) between 0 and 4. What graphing window allows you to see values of \(f(t)\) that correspond to these values of \(t\)?

Function \(g\) gives the amount of a drug in a dog's body, in milligrams, \(t\) hours since the veterinarian administered it. The equation \(g(t) = 600 \boldcdot \left(\frac{3}{5}\right)^t\) defines this function.

1. What does the fraction \(\frac{3}{5}\) mean in this situation?
2. Sketch a graph of \(g\).
3. What are the domain and range of \(g\)? Explain what they mean in this situation.

The dollar value of a moped is a function of the number of years, \(t\), since the moped was purchased. The function, \(f\), is defined by the equation \(f(t) = 2,\!500 \boldcdot \left(\frac{1}{2}\right)^t\) .

What is the best choice of domain for the function, \(f\)?

A patient receives 1,000 mg of a medicine. Each hour, \(\frac{1}{5}\) of the medicine in the patient's body decays. 

The trees in a forest are suffering from a disease. The population of trees, \(p\), in thousands, is modeled by the equation \(p = 90 \boldcdot \left(\frac{3}{4}\right)^t\), where \(t\) is the number of years since 2000.

1. What was the tree population in 2001? What about in 1999?
2. What does the number \(\frac{3}{4}\) in the equation for \(p\) tell you about the population?
3. What is the last year when the population was more than 250,000? Explain how you know.

1. Is the birth date, \(b\), a function of the student, \(s\)?
2. Is the student, \(s\), a function of the birth date, \(b\)?

Mai wants to graph the solution to the inequality \(5x - 4 > 2x - 19\) on a number line. She solves the equation \(5x - 4 = 2x - 19\) for \(x\) and gets \(x = \text -5\).