Exponential functionsIB MYP Maths Extended: Mind map

Exam questions on Exponential functions

1. Consider the exponential function $f(x)=3^x$.
   Solve $3^x=\frac{1}{27}$.2 marks
2. A car is bought for \24,000$. Its value$V$dollars after$t$years is modelled by$V=24,000\times0.85^t$.
   Write down the equation of the horizontal asymptote of the graph of $V$ against $t$, and explain what it tells you about the value of the car.2 marks
3. A biologist counts the bacteria in a culture each hour. At the start there are 500 bacteria; after 1 hour there are 600, after 2 hours 720 and after 3 hours 864.
   Show that the growth is exponential and find a model of the form $N=a\times b^t$ for the number of bacteria $N$ after $t$ hours.3 marks