There are 30 NRICH Mathematical resources connected to Exponential and logarithmic functions, you may find related items under Coordinates, functions and graphs.
Broad Topics > Coordinates, functions and graphs > Exponential and logarithmic functions
Can you work out which processes are represented by the graphs?
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Investigate the mathematics behind blood buffers and derive the form of a titration curve.
Can you locate these values on this interactive logarithmic scale?
Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?
The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.
If a sum invested gains 10% each year how long before it has doubled its value?
Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
Explore the properties of these two fascinating functions using trigonometry as a guide.
A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How does the half-life of a drug affect the build up of medication in the body over time?
In this question we push the pH formula to its theoretical limits.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Compares the size of functions f(n) for large values of n.
Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?
What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.
This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.
Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.
Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.
In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.
Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?