找到你今天要练的题。

The exponential function \( f \) is defined by \( f\left(x\right)=ab^x \) , where a and b are positive constants. If \( f\left(s\right)=t \) and \( f\left(s+1\right)=t-0.87t \), where s and t are constants, what is the value of b?

\( C(t)=240(\frac{54}{53})^{t−14}+7 \) 
The function C gives the estimated number of cephalopods, a class of marine animal, in a certain area, where t is the number of months since a study began. How many months after the study began was the number of cephalopods in the area estimated to be 247?

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 predicted population of a city x years after 1982, where \( x\le10 \), can be modeled by the function \( f(x)=47,000(1.04)^x \). Which of the following is the best interpretation of the statement “\( f(6) \) is approximately equal to 59,470” in this context?

The function \( f(t)=40,000(2)^{\frac{t}{410}} \)  gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

\( f\left(x\right)=3,000\left(0.75\right)^x \) 
A conservation scientist implemented a program to reduce the population of a certain species in an area. The given function estimates this species' population x years after 2008, where \( x\le8 \). Which of the following is the best interpretation of 3,000 in this context?

Two variables, x and y, are related such that for each increase of 1 in the value of x, the value of y increases by a factor of 4. When \( x=0 \) , \( y=200 \) . Which equation represents this relationship?

A scientist initially measures 12,000 bacteria in a growth medium. 4 hours later, the scientist measures 24,000 bacteria. Assuming exponential growth, the formula \( P=C\left(2\right)^{rt} \) 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?

The population of the town of Smithville doubled every 75 years from 1659 to 1959. The population of this town was 240,000 in 1959. What was the population of this town in 1659?

There are 240 players in a tennis competition that includes 4 rounds of matches. Each player in the competition will play a match against another player in round 1. At the end of each round, the player who loses the match is eliminated and the player who won the match advances to the next round to play a match against another winning player. Which equation gives the number of players, p, eliminated at the end of round r, where \( r\le4 \)?

\( y=3,600\left(a\right)^x \) 
The given equation, where \( a \) is a positive constant, gives the predicted number of bacteria,\( y \), in a growth medium \( x \) hours after the number of bacteria was initially measured. According to the equation, what was the predicted number of bacteria initially measured in the growth medium?

The number of bacteria in a liquid medium doubles every day. There are 44,000 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?