找到你今天要练的题。

The value of a collectible item increased by the same percentage every year between 2000 and 2007. In 2000, the value of the collectible item was $40, and in 2002, the value of the collectible item was $48.40. What was the value, in dollars, of this collectible item in 2007?

\( P(t)=67\left(\frac{5}{4}\right)^t \)
A reindeer population was introduced into an area and researched for 19 years. Function P models this reindeer population t years after the population was introduced into the area. Which statement is the best interpretation of \( \frac{5}{4} \) in this context?

\( C(t)=220\left(\frac{52}{51}\right)^{t-12}+8 \) 
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 228?

\( f(x)=28(1.40)^{\frac{x}{3}} \) 
For the given function \( f \), the value of \( f(x) \) increases by p% for every increase of x by 6. What is the value of p?

For the exponential function g, the value of \( g(x) \) doubles for every increase of 2 in the value of x. If \( g(4)=9 \), what is the value of \( g(6) \)?

A certain investment account offers a special interest rate for the first 4 months the account is open followed by a lower interest rate for the remainder of the time the account is open. Bennett opened one of these accounts with an original account balance of $700 and did not make any other deposits or withdrawals. 4 months after Bennett opened the account, the balance had increased by 0.6% of the original balance. 6 months after Bennett opened the account, the balance had increased by an additional 0.2% of the balance at the end of the first 4 months. Every 2 months after the first 6 months, the balance had increased by an additional 0.2% of the balance 2 months before. Which of the following equations could represent the account balance \( B(x) \), in dollars, x months after the account was opened, where \( x\ge4 \)?

An exponential function \( f \) gives the estimated amount of an X-ray beam's initial intensity remaining after passing through a w-centimeter-thick window made of beryllium. The function estimates that after passing through a 1.2-centimeter-thick window, the amount of the X-ray beam's initial intensity remaining is 0.74. Which equation could define ?

The equation \( E(t)=3(1.2)^t \)  gives the estimated number of employees at a certain business, where t is the number of years since the business opened. Which of the following is the best interpretation of the number 3 in this context?

The equation \( E(t)=3(1.7)^t \) gives the estimated number of employees at a certain business, where t is the number of years since the business opened. Which of the following is the best interpretation of the number 3 in this context?

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

An exponential model for the number of squirrels in a certain area estimates that there were 200 squirrels in the area in the year 2003, and that at the end of each 4-year period for the next 20 years, the number of squirrels in the area was 120% more than the number at the end of the previous 4-year period. Which of the following equations represents this model, where N is the estimated number of squirrels in this area t years after 2003, and \( 0\le t\le20 \)? 

James purchased a certain baseball card on January 1. The function \( f(x)=85(1.03)^x \), where \( 0\le x\le10 \) , gives the predicted value, in dollars, of the baseball card x years after James purchased it. What is the best interpretation of the statement "\( f(8) \)  is approximately equal to 108" in this context?