1003064106
Level:
C
Find the solution of the following inequality.
\[ 5^x\geq3^x \]
\( x\in[0;\infty) \)
\( x\in[1;\infty) \)
\( x\in\{0\} \)
no solution
C
1103064105
Level:
C
Decide which of the following diagrams shows the solution set of the given inequality.
\[ 16\cdot4^{2x-3} < 64^{x+1} \]
1003064104
Level:
C
How many solutions in the set of positive integers does the following inequality have?
\[ \left(\frac34\right)^{x+1}\leq\left(\frac43\right)^{3-2x} \]
\( 4 \)
\( 5 \)
\( 1 \)
\( 0 \)
1003064103
Level:
C
Find the solution set of the following inequality.
\[ \left(\frac12\right)^x\geq\left(\frac18\right) \]
\( x\in(-\infty;3] \)
\( x\in(3;\infty) \)
\( x\in(-\infty;3) \)
\( x\in[3;\infty) \)
1003064102
Level:
C
How many solutions does the following inequality have?
\[ 5^x < 0 \]
No solutions
Infinitely many solutions
Exactly one solution
Exactly two solutions
1003064101
Level:
C
Find the solution of the following inequality.
\[ 2^x\geq1 \]
\( x\in[0;\infty) \)
\( x\in(0;\infty) \)
\( x\in(-\infty;0) \)
\( x\in(-\infty;0] \)
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.
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, \( p=12.0\cdot(0.88)^t \)
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, \( p=12.0\cdot(1.12)^t \)
1003082607
Level:
C
Find the set of all solutions of the following inequality.
\[ 4^{x+3}-2\cdot5^{x+2} < 5^{x+2}+4^{x+1} \]
\( (-1;\infty) \)
\( (-\infty;-1) \)
\( (1;\infty) \)
The inequality has no solution.