• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Investigate the mathematical functions which model these curves and determine Logans logo

Extracts from this document...


In this assignment, I will investigate the mathematical functions which model these curves and determine Logan’s logo.

For this, I will use an appropriate set of axis with a scale of 1 centimetre per unit and record a number of different data points on the curves which will then create model functions.

Logan’s logo represents two curves: the lower curve and the upper curve. The variables used are the horizontal-axis and the vertical-axis.

The measured numbers of data points for the lower and upper curve are represented in this table.

1. The various numbers of data points from the curve are entered in a table as shown below. L1 being the horizontal-axis, L2 the lower curve and L3 the upper curve.


The window parameters for the graph are then programmed for both the upper and the lower curve to respect the scale on Logan’s logo:


Then a scatterplot is obtained for both curves after putting the points of each curve into a table.


Graph of the lower curve:


...read more.


Using the sinusoidal regression formula the values of a, b, c and d for the upper sine curve are found:


Following the sine formula, the letters are replaced with the values found with the sinusoidal regression formula in the function plot to then create a graph for each curve.


The graph of the lower sine curve resembles this:


The same method is replicated for the second upper sine curve:


The graph of the upper sine graph is represented as the following:


The amplitude of the upper sine curve is calculated with the following formula: image16.png

However, the sine curves of Logan’s logo carry some limitations.

First of all, it is not certain that this curve follows the sinusoidal behaviour. It is only a possible hypothesis. Furthermore, the values are not extremely precise therefore the results of the sine equations are not very accurate. Thirdly, as it was graphically impossible to obtain the correlation coefficient (r),

...read more.



The amplitude is measured with the following formula:



ower limit=0

Upper limit=8

3. For the business card, we must multiply the amplitude by 5/8 and to find the area between two curves, we find the area under the curve which is above and subtract the area of the curve which is below.

The lower limit is 0 and the upper one is 8.  (screenshot 2nd calc , 7)

In order to find the area between the two curves, we have to substract the area of the lower curve to the area of the upper curve.


The business card’s area is 45cm2. The amplitude of the two sine functions must be multiplied by image25.png to reduce the height (y-axis) to 5 cm

Logan’s logo occupies image26.png of the business card.

Pour la 1ère function A has to be multiplied by 5/8 and d which affects vertical translation  ce qui donne 1.27 et d= 2.42*5/8=1.51

Pour la 2ème function a (amplitude) and the d by 5/8 2.93 * 5/8=1.89. et d=4.03*5/8=2.52

Screenshots of business-card format, sine functions :

Then calculate the integrals and area

Sine function 1: aimage21.png

image27.png for the lower curve

For the upper curve f(x)=2axsin(bx+c)d

image28.png cm 2 for the upper curve.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Derivative of Sine Functions

    gradient of f(x) =-sinx.at every /4 unit 2 when a=-2f(x) =-2sinx The value of the gradient of f(x) =-2sinx. At every /4 unit is shown in the table below: X -2 - - - - - - - 0 -2.00 -1.41 0 1.41 2.00 1.41 0 -1.41 -2.00 X 2 -1.41 0 1.41

  2. Investigating Sin Functions

    did NOT shrink it vertically like we noticed above. In fact, it reflected it across the x axis, and kept the wave the same. To make this change easier to notice, refer to the graph below, made on FooPlot, of both graphs in the same window: Red = -1sin(x), Black = sin(x)

  1. An investigation of different functions that best model the population of China.

    This can be seen below. As one can see from the graph, the researcher's model fits the original data relatively accurately, however, being an exponential model, it does not reflect the points in which the original data slows and down and instead increases at a fairly constant rate.

  2. A logistic model

    2.2)un ? (?2 ?10?5 )(u )(u ) ? 2.2u The logistic function model for un+1 is: n n n ? (?2 ?10?5 )(u 2 ) ? 2.2u ?5 2 un?1 ? (?2 ?10 )(un ) ? 2.2un {5} b. For r=2.3. One can write two ordered pairs (1?104 , 2.3)

  1. Math IA - Logan's Logo

    points on the curve, which are (1.8, 3.5) and (-1.6, -2.8) respectively. When we find the amplitude of a sine curve, we can disregard the x-values, as they do not tell us anything about the height of the curve. Now that we've found the highest and lowest points of the

  2. LACSAP's Functions

    0 0 1 1 1 1 1 1 1 1 1 Comparing the new triangle to Pascal's Triangle, it almost appears that the new triangle is a mirror image of Pascal's triangle. Using this new information, I decided to plot the row numbers of LACSAP's triangle against r = 1

  1. Logan's logo

    applied to model functions that follow the behavior of each curve shown. We can notice from the graph that these two curves are parallel to each other hence they might follow the same type of equation but vary in the parameters values.

  2. Statistics project. Comparing and analyzing the correlation of the number of novels read per ...

    The 30 girls surveyed: Modal mark is 61-80. Most read a higher amount of books of 2 per week than boys, but is still quite low. Their median value for the marks is 40-60 and their average mark is 66.7.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work