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.

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 ?

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.

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.

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. . . .

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?

Log Attack

Age 16 to 18
Challenge Level

Solve these equations.

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.

Integral Equation

Age 16 to 18
Challenge Level

Solve this integral equation.

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.

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.

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?

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.

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.

Power Match

Age 16 to 18
Challenge Level

Can you locate these values on this interactive logarithmic scale?

How Does Your Function Grow?

Age 16 to 18
Challenge Level

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

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.

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?

Mixing Ph

Age 16 to 18
Challenge Level

Use the logarithm to work out these pH values

Big, Bigger, Biggest

Age 16 to 18
Challenge Level

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

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?