The exponential function e^xEdexcel International A Level Maths: Mind map

Exam questions on The exponential function e^x

1. The function $f$ is defined by $f(x)=e^{2x-1}+3$ for all real $x$.
   Write down the range of $f$ and give a reason why $f(x)$ can never equal $3$.2 marks
2. The mass $M$ grams of a radioactive sample is modelled by $M=80e^{-0.05t}$, where $t$ is the time in hours after the sample was first measured.
   Find the time at which the mass of the sample is $20$ g. Give your answer in hours to 3 significant figures.2 marks
3. The curve $C$ has equation $y=e^{3x}-5$ and the line $l$ has equation $y=20$.
   Find the exact coordinates of the points where $C$ crosses the coordinate axes.3 marks