Resources tagged with: Exponential and Logarithmic Functions

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There are 26 results

Broad Topics > Coordinates, Functions and Graphs > Exponential and Logarithmic Functions

Gosh Cosh

Age 16 to 18 Challenge Level:

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

What Do Functions Do for Tiny X?

Age 16 to 18 Challenge Level:

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

Prime Counter

Age 16 to 18 Challenge Level:

A short challenge concerning prime numbers.

Cobalt Decay

Age 16 to 18 Challenge Level:

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

Complex Sine

Age 16 to 18 Challenge Level:

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.

Log Attack

Age 16 to 18 Challenge Level:

Solve these equations.

Integral Equation

Age 16 to 18 Challenge Level:

Solve this integral equation.

Equation Attack

Age 16 to 18 Challenge Level:

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.

Hyperbolic Thinking

Age 16 to 18 Challenge Level:

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

Quorum-sensing

Age 16 to 18 Short Challenge Level:

This problem explores the biology behind Rudolph's glowing red nose.

Harmonically

Age 16 to 18 Challenge Level:

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

What Are Complex Numbers?

Age 16 to 18

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. . . .

How Does Your Function Grow?

Age 16 to 18 Challenge Level:

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

Function Pyramids

Age 16 to 18 Challenge Level:

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?

Exponential Trend

Age 16 to 18 Challenge Level:

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.

Sierpinski Triangle

Age 16 to 18 Challenge Level:

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.

Tuning and Ratio

Age 16 to 18 Challenge Level:

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

Mixing Ph

Age 16 to 18 Challenge Level:

Use the logarithm to work out these pH values

Ph Temperature

Age 16 to 18 Challenge Level:

At what temperature is the pH of water exactly 7?

Extreme Dissociation

Age 16 to 18 Challenge Level:

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

Blood Buffers

Age 16 to 18 Challenge Level:

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

Big, Bigger, Biggest

Age 16 to 18 Challenge Level:

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

Drug Stabiliser

Age 16 to 18 Challenge Level:

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

Power Match

Age 16 to 18 Challenge Level:

Can you locate these values on this interactive logarithmic scale?

Infinite Continued Fractions

Age 16 to 18

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

Dating Made Easier

Age 14 to 16 Challenge Level:

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