Exponential functions and e^xEdexcel A-Level Maths: Mind map

Exam questions on Exponential functions and e^x

1. A function is given by $f(x)=a^x$, where $a>0$, and its graph passes through the point $(2,\,25)$.
   Solve $f(x)=\dfrac{1}{125}$.2 marks
2. Consider the curve $y=e^{2x-1}+3$.
   Explain why the curve never crosses the $x$-axis.2 marks
3. The mass $M$ grams of a radioactive sample $t$ days after it is first measured is modelled by $M=80e^{-0.05t}$.
   Find $\dfrac{dM}{dt}$ and hence show that the rate of change of $M$ is proportional to $M$.3 marks