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The population of a certain city doubled every 75 years from 1666 to 1966. The population of this city was 240,000 in 1966. What was the population of this city in 1666?

\( y=7,700\left(0.85\right)^x \) 
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?

\( y=500\left(2\right)^{2x} \) 
The equation gives the estimated number of online newsletter subscribers at the end of every six-month period, x, starting from the end of January 1995, where \( 0\le x\le4 \) . Which statement is the best interpretation of the y-intercept of the graph of this equation in the xy-plane?

James purchased a certain baseball card on January 1. The function \( f\left(x\right)=55\left(1.04\right)^x \), where \( 0\le x\le10 \), gives the predicted value, in dollars, of the baseball card \( x \)x years after James purchased it. What is the best interpretation of the statement “\( f\left(7\right) \)  is approximately equal to 72” in this context?

\( P\left(t\right)=260\left(1.03\right)^{\left(\frac{3}{2}\right)t} \) 
The function P models the population, in thousands, of a certain city t years after 2009. According to the model, the population is predicted to increase by n% every 8 months. What is the value of n?

\( f\left(x\right)=7,000\left(0.90\right)^x \) 
A conservation scientist implemented a program to reduce a certain invasive insect population in an area. The given function estimates this insect species' population x years after 2008, where x \( \le \)  8. Which of the following is the best interpretation of 7,000 in this context?

The function f is defined by \( f\left(x\right)=41\left(0.28\right)^x \) . 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?

A certain neighborhood had a population of 1,170 in 2006. Each year for the next 5 years, the population of the neighborhood increased by approximately 3% of the population the previous year. Which of the following equations represents the population, N , of the neighborhood t years after 2006, where t ≤5?

The predicted number, B(t), of a certain type of bacterial cell in a growth medium is given by the function B(t) = 90(2)^t, where t is the time, in days,since the number of bacterial cells was first measured. Which of the following is the best interpretation of B(4)= 1,440 in this context?

\( f\left(x\right)=8,000\left(0.75\right)^x \) 
A conservation scientist implemented a program to reduce a certain invasive insect population in an area. The given function estimates this insect species' population  x years after 2008, where x \( \le \) 8. Which of the following is the best interpretation of 8,000 in this context?

A sample of a certain isotope takes 29 years to decay to half its original mass. The functions \( s(t)=184(0.5)^{\frac{t}{29}} \)  gives the approximate mass of this isotope, in grams, that remains t years after a 184-gram sample starts to decay. which statement is the best interpretation of s(87)= 23 in this context?

The number of bacteria in a liquid medium doubles every day. There are 48,000 bacteria in the liquid medium at the start of an observation. Which represents the number of bacteria, y, in the liquid medium t days after the start of the observation?