Exponential functionsAQA A-Level Maths: Mind map

Exam questions on Exponential functions

1. The curve $C$ has equation $y=2^x$.
   Find the $x$-coordinate of each point where $C$ meets the lines $y=16$ and $y=\frac18$.2 marks
2. The number $N$ of bacteria in a culture, $t$ hours after it is first measured, is modelled by $N=500e^{0.4t}$.
   Find the rate of increase of the number of bacteria when $t=5$, giving your answer to 3 significant figures.2 marks
3. The curve $C$ has equation $y=e^{2x}$ and passes through the point $P$ where $x=\frac12$.
   Find the exact coordinates of $P$ and the exact gradient of $C$ at $P$.3 marks