Math topic中文

Exponential functions

graphs of exponential functions y=kaxy = ka^{x}, where aa is a positive integer

Practice questions

  1. 1The equation of a curve is y=x2e2xy = x^2 e^{2x}. Obtain an expression for dydx\dfrac{dy}{dx}. Find the range of values of xx…
  2. 2已知函数f(x)f\left(x\right)是定义在RR上的偶函数，且f(0)=0f\left(0\right)=0，当x>0x>0时，f(x)=log⁡2(x+1).(1)f\left(x\right)={{\log}_{2}}\left(x+1\right).(1)…
  3. 3The number of bacteria in a colony doubles every hour. The colony starts with: 50 bacteria. The table below shows the nu…
  4. 4The sketch shows the graph of y=ka−xy = ka^{-x}. The points A (−1, 6) and B (0, 3) lie on the graph. Find the value of k and…
  5. 5Sketch the graph of y=2ln⁡xy = 2\ln x. In order to solve the equation xe2x=13xx e^{2x} = \dfrac{1}{3x}, a suitable straight line ha…
  6. 6设不等式∣4x−a∣>∣1−2x+3∣\left|{{4}^{x}}-a\right|>\left|1-{{2}^{x\text{+3}}}\right|对所有x∈[1,2]x\in[1,2]均成立，则实数aa的取值范围是()(\quad) A. a<−15a< -15…
  7. 7Sketch the graph of y=2x2y=\frac{2}{x^2} on the axes below. The point (1, 1) is shown in the diagram. Answer ... Sketch the…
  8. 8A vaccine was introduced to a virus in an experiment. The number, N, of virus t hours after being introduced to the vacc…
  9. 9Sketch the graph of y = 3^{-x} on the axes below. Indicate clearly the coordinates of the points where the graph crosses…
  10. 10The diagrams A, B, C, D, E and F show six graphs of different functions. yy is inversely proportional to xx, Diagram .…
  11. 11已知幂函数f(x)=(m−1)2xm2−4m+2f(x){=}{(m{-}1)}^{2}x^{m^{2}{-}4m{+}2}在(0,+∞)(0{,}{+∞})上单调递增，函数g(x)=2x−tg(x){=}2^{x}{-}t，对于任意的x1∈[1,6)x_{1}{∈[}1{,}6)，总存在x2∈[1,6)x_{2}{∈[}1{,}6)…