Exponential functionsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

What is the general form of an exponential function?
What point do all graphs of y=a^x pass through?
What is the horizontal asymptote of y=a^x?
When does y=a^x show growth and when decay?
Can y=a^x ever be zero or negative?
Evaluate 2^{-3}.
What growth factor represents an increase of 8%?
What growth factor represents a decrease of 15%?
Write the compound interest formula.
How does simple interest differ from compound interest?
How can you check that data is exponential?
How can technology solve 500\times1.2^t=5000?
Why can an exponential model be unreliable far from the data?

Exam questions on Exponential functions

Consider the exponential function $f(x)=3^x$ .
Solve $3^x=\frac{1}{27}$ .2 marks
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).