Or search by topic

There are **30** NRICH Mathematical resources connected to **Exponential and logarithmic functions**, you may find related items under Coordinates, functions and graphs.

Problem
Primary curriculum
Secondary curriculum
### What's That Graph?

Can you work out which processes are represented by the graphs?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Back Fitter

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?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Blood Buffers

Investigate the mathematics behind blood buffers and derive the form of a titration curve.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Power Match

Can you locate these values on this interactive logarithmic scale?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Harmonically

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Legacy

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Equation Attack

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dating Made Easier

If a sum invested gains 10% each year how long before it has doubled its value?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Exponential Trend

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hyperbolic Thinking

Explore the properties of these two fascinating functions using trigonometry as a guide.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Function Pyramids

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Very Shiny Nose?

This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cobalt Decay

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stirling Work

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Drug Stabiliser

How does the half-life of a drug affect the build up of medication in the body over time?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Extreme Dissociation

In this question we push the pH formula to its theoretical limits.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Do Functions Do for Tiny X?

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Does Your Function Grow?

Compares the size of functions f(n) for large values of n.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tuning and Ratio

Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sierpinski Triangle

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.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### What Are Complex Numbers?

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.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Complex Sine

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gosh Cosh

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Infinite Continued Fractions

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Big, Bigger, Biggest

Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?

Age 16 to 18

Challenge Level