Exponential functions

1103082501

Level: 
C
Mary purchased a new car at the purchase price \( 12\,000 \) EUR. Depreciation rate of the car is \( 12\% \) per year. Suzy purchased a new car at the same time as Mary and the purchase price was \( 14\,500\) EUR. The depreciation rate of Suzy's car is \( 15\% \) per year. Let \( p \) be the price of the car in thousands euros and \( t \) be the age of the car in years. Which of the following legends is correct for the next graph?
Suzy's car, \( p=14.5\cdot(0.85)^t \)
Mary's car, \( p=12.0\cdot(0.88)^t \)
Suzy's car, \( p=14.5\cdot(1.15)^t \)
Mary's car, \( p=12.0\cdot(1.12)^t \)

1103082502

Level: 
C
Mary purchased a new car. The purchase price was \(12\,000\) euros and the value of the car depreciates by \( 12\% \) per year. Suzy purchased a new car at the same time as Mary and the purchase price was \( 14\,500 \) euros. The depreciation rate for Suzy's car is \( 15\% \). Let \( p \) be the price of the car in thousands euros and \( t \) be the age of the car in years. In the diagram below, determine the color of the graph that shows relationship between the price of Mary's car and its age. (Note: The answers include not only the color of the graph but also the relevant function equation.)
green, \( p=12.0\cdot(0.88)^t \)
yellow, \( p=14.5\cdot(1.15)^t \)
orange, \( p=12.0\cdot(1.12)^t \)
blue, \( p=12.0\cdot(0.88)^t \)

1103082503

Level: 
C
At year \( 2000 \) (\(t=0\)) a small village has a population of \( 350 \) people. The graph in the picture below shows the population function for the next \( 50 \) years. One of the following statements is true. Which one is it?
The village population declines by \( 3.8\% \) per year.
The village population grows by \( 3.8\% \) per year.
The village population declines by \( 5 \) people per year.
The village population grows by \( 5 \) people per year.

1103082704

Level: 
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is true.
\( f(x)=2^{|x|};\ x\in[-2;2] \)
\( f(x)=\left|2^x\right|;\ x\in[-2;2] \)
\( f(x)=\left|x^2+1\right|;\ x\in[-2;2] \)
\( f(x)=\left|2^{-x}\right|;\ x\in[-2;2] \)

9000003607

Level: 
C
The function \(f(x) = \left (\frac{1} {3}\right )^{x}\) is graphed in the picture. Identify a possible analytic expression for the function \(g\).
\(y = 3^{|x|}- 1\)
\(y = \left |\left (\frac{1} {3}\right )^{x} - 1\right |\)
\(y = \left (\frac{1} {3}\right )^{|x|}- 1\)
\(y = \left (\frac{1} {3}\right )^{|x-1|}\)
\(y = \left |3^{x} - 1\right |\)
\(y = 3^{|x-1|}\)