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The function \( f \) is defined by \( f(x)=55(0.12)^x \). For any positive integer n, the value of \( f(n) \) is \( p\% \) less than the value of \( f(n−1) \). What is the value of p?

\( y=7,200(0.85)^x \) 
The given equation estimates the value, in dollars, of a certain car x years after it was purchased. According to the given equation, what was the estimated value, in dollars, of the car at the time it was purchased?

At different times on a certain day, a manager at a theme park recorded the number of visitors. An exponential model gives the estimated number of visitors, V, at the theme park t hours after the theme park opened, where t ≤ 3. Based on the model, 85 visitors were estimated to be at the theme park when it opened, and every 30 minutes the estimated number of visitors increased by 120% of the estimated number of visitors 30 minutes earlier. Which of the following equations best represents this model?

\( P(t)=22.5(1.036)^t \) 
The function P gives the predicted population, in millions, of a certain country for the period from 1984 to 2018. where t is the number of years after 1984.
According to this function, what is the best interpretation of the statement “P(8) is approximately equal to 29.86”?

An environmental scientist studies the decomposition of paper bags when the bags are placed in an environment with a certain type of bacteria. The exponential function \( f(x)=545(0.91)^x \) gives the estimated remaining mass, in grams, of the paper bags x days after they are placed in an environment with this bacteria, where \( 0\le x\le30 \). If this function is graphed in the xy-plane, where \( y=f(x) \), which statement is the best interpretation of the point (1, 495.95) on the graph?

For an online trivia game, 300 points are awarded for a correct answer if a question is answered in less than 4 seconds from the time the question is asked. Each 4 seconds after the question is asked, the number of points awarded for a correct answer decreases by 15% of the number of points awarded for a correct answer in the previous 4 seconds. Which function gives the number of points awarded for a correct answer x seconds from the time the question is asked, where x is a multiple of 4?

A scientist initially measures 6,000 bacteria in a growth medium. 4 hours later, the scientist measures 12,000 bacteria. Assuming exponential growth, the formula \( P=C2^{rt} \) gives the number of bacteria in the growth medium, where r and C are constants and P is the number of bacteria t hours after the initial measurement. What is the value of r?

A computer program models the total mass of the population of a certain type of algae after the algae was placed in an environment where it has no natural predators. According to the model, the estimated total mass of this population of algae at the end of every 6‑hour period is 129% greater than the estimated total mass of this population of algae at the end of the previous 6‑hour period, and the estimated total mass of this population of algae is 613.90 grams after 18 hours. Which equation best represents this model, where A is the estimated total mass, in grams, of the population of algae after x hours, and x < 50?

A sum of 9,000 dollars was invested in a certificate of deposit (CD) that earns interest, and no other deposits or withdrawals were made after that. The function \( f(x)=9,000(1+0.03)^x \) gives the value of the CD, in dollars, x years after the investment was initially made, where \( x\le5 \). Which of the following is the best interpretation of the statement "\( f(2) \) is approximately equal to 9,474.08" in this context?

A researcher observes a sample of a nuclide. An exponential model estimates that the mass, in grams, of the sample decreases by 21% every 19.72 minutes. Which of the following equations could represent this model, where M is the estimated mass, in grams, of the sample t minutes after the researcher began observing the sample?

The function \( f(x)=217(1.030)^x \) models the value, in dollars, of a certain bank account from 1957 through 1972, where x is the number of years after the end of 1957. Which of the following is the best interpretation of "\( f(5) \) is approximately equal to 252" in this context?

The function \( f\left(x\right)\ =\ 900\left(0.5\right)^{\frac{x}{12}} \) gives the predicted intensity of a beam \( f\left(x\right)\ \) , in number of photons in the beam,  \( x\ \) millimeters below the surface of a certain material. What is the best interpretation of \( f\left(12\right)=450\ \) ?