







A model of the sun and the Earth 
20140614 

From Lynn: There is a model of the sun that is 2 1/2 inches in diameter. This is the only clue we have! How far away is the earth from this model? Answered by Penny Nom. 





The spread of a rumor 
20120409 

From Roohi: The function f(t) = a/(1+3e^(bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents. Answered by Penny Nom. 





Sales as a function of advertising 
20101208 

From Adori: The sales S(in thousands if units) of a product after x hundred dollars is spent on advertising is given by S=10(1e^kx). Find S as a function of x if 2500 units are sold when $500 is spent on advertising. Answered by Penny Nom. 





A linear relationship 
20100622 

From Laura: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $300 to drive 480 miles and in June it cost her $460 to drive 800 miles.
Question: Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. Answered by Robert Dawson. 





A scale model of a city 
20100518 

From Briana: Well I have to create a three dimensional city for a geometry project and it requires us to use precise scal factor and well we want to build a medium sized city but our teacher said that If we make or buildings to high our houses would look like super small compared to the tall building were trying to figure out if we were to build a medium sized city what scale factor should we use to make the houses big enough to see and design? Answered by Walter Whiteley and Tyler Wood. 





Modelling an underpass 
20100511 

From Sue: An engineer at the Ministry of Transport is creating the plans for a new road. This road
will cross the path of a busy railway track so it will be necessary to built an underpass for this road.
This underpass will be in the shape of a parabolic arch.
The specifications include:
the road must be at least 10 m wide and it must have shoulders at least 2 m wide on either
side of the road.
there must be a clearance of 3 m over all areas of the road.
What quadratic equation could you use to model this bridge. Answered by Penny Nom. 





A model for the population of a Canadian city 
20100407 

From jess: Let t^2 represent tsquared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007.
a) According to the model, what will the population be in 2010?
B) In what year is the population predicted to be 300,000? Answered by Penny Nom. 





A linear relationship 
20100224 

From Mel: This table shows the linear relationship between an aeroplane's height (above sea level) and the outside air temperature.
h (cm) 
120 
340 
480 
600 
1040 
T (degrees C) 
14.28 
12.96 
12.12 
11.4 
8.76 
Find the gradient and vertical intercept of the function. Write the formula for T. Answered by Penny Nom. 





A 3D cardboard cupcake 
20100130 

From Margaret: Hi,
I'm an art student and I'm attempting to build a 3D cupcake out of cardboard.
I want it to have a circular base of 8.5 inches and sides that are 7'' tall and slope outward so the top of the base is 29'.
The top with the frosting would be a detachable lid made from a cone with a base circumfrance of 29".
My problem is how to cut the side so they will slope out, I'm pretty sure there needs to be a curve, however I don't how to calculate the degree of it.
Ideally I want the sides to be a single piece of cardboard.
I also don't know how to calculate the arc needed to make a cone who's circular base's circumfrence is 29''.
Thanks,
Margaret Answered by Stephen La Rocque. 





Constructing a scale model 
20090927 

From Colleen: What is the formula i need to use to find out how to state a reasonable scale in the question below;
Suppose you were constructing a model that must sit on a piece of cardboard that is 22cm by 28cm. STATE THE REASONABLE SCALE that you can use to build a model to represent the following items. Determine the dimensions of the model.
a) a rectangular prism with a length of 5m and a width of 2m? Answered by Penny Nom. 





Fitting the curve y=a*exp(b*x)+c 
20090812 

From aika: Could one show me the complete algorithm and formula for finding the coefficients (a,b, and c) in exponential regression model
y=a*exp(b*x)+c Answered by Robert Dawson. 





Math in everyday life 
20090803 

From Naveen: Dear sir,
We are advised to do a project on "Mathematical modeling to solve various problems
of our everyday life/environmental related problems...... Can u plz help us by mailng some
ideas, suggestion,reference to make my project successful.... Thanking you......
Waiting for your favourable reply...... Answered by Penny Nom. 





The scale for a model train 
20090313 

From Shelly: Lindy is planning to build a model of a train using a scale where 2 inches represents 25ft. If the train is 60 feet long, what is the length in inches that Lindy should build the model of the train? Answered by Stephen La Rocque and Penny Nom. 





A linear model 
20080509 

From Shelby: How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of 25,195 per year with t represents the number of years since 1994? Answered by Penny Nom. 





A model for a building 
20070717 

From Carl: A model for a building is 50 centimeters long, 38 centimeters wide, and 225 centimeters tall
on model 1 centimeter represents 2.5 meters.
I need to find the volume of the actual building in cubic meters,and the surface area of the building including
ceilings and floors. round to the nearest tenth of a square meter. Answered by Harley Weston. 





A scale model 
20061130 

From Adrianna: 1) A model of a storage compartment is to a scale of 1:40. If the surface area of the model is 25 square centimeters, what is the surface area of the actual storage compartment?
a) The storage compartment in the last question has an actual volume of 8 cubic metres. What is the volume of the model? Answered by Penny Nom. 





A scale factor 
20060325 

From Jackie: I need a formula or step by step help to show my child how to find missing dimensions for example: The scale factor for a model is 10 inches = ________ feet
Model 39.7 in
Actual 11.9 ft Answered by Penny. 





A train model is created using a scale of 1:60 
20060101 

From Jennifer: An "n gauge " train model is created using a scale of 1:60. If an actual train engine, the "K4" an early twentiethcentury engine,is 45 feet long, what is the length of an "N gauge" model of the engine in inches? Answered by Penny Nom. 





Modelling monthly temperature with a cosine 
20041225 

From Regis: The average monthly temperature for a location in Ontario as a function of month number can be modelled using the equation y = a cos[k(t + b)] + d. Answered by Harley Weston. 





The best linear model 
20010729 

From Rebeca: I am a student (senior) summer hire working for Dept of the Army Resource Management. I've been assisting the Analyst in developing a model to predict training costs. The technique we used was simple linear regression. Now I've been asked for my opinion in choosing the best model I feel is better. I've chosen #1. Garrison Training but I want a second opinion before I give my choice. I've taken basic statistics last year in high school and will probably be taking more this year. Could you look over the information and give me a reason my choice would not be best? The dep variabley, is Training costs in dolars per day. Model  Ind Variable X  a  b  r  sy.x  1.  Garrison Training  126.31  0.982  0.9055  117.2  2.  Local Training  212.16  1.37  0.7937  142.7  3.  Man Rig Area  116.38  2.47  0.6481  175.6  4.  Major Training  346.12  4.67  0.7280  167.2  Answered by Andrei Volodin. 





Conservation, consumption and population growth 
20010604 

From Steve: I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 41990 to 33,871 in 42000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: . . . Answered by Penny Nom. 





Toy bricks 
20010513 

From Sarah: A regularsized brick weighs 4 kilograms. How much will a similar toy brick, made of the same material, but all of the same dimensions of which are four times smaller, weigh? The 300metre tall Eiffel tower is made of steel and weighs 8 000 000 kg. An exact replica, made of the same material, weighs 1 kg. How high is the replica Answered by Penny Nom. 





A model area 
19991215 

From John Ost: Hello, I am a college student taking an elementary math course I need if possible assistance to developing an area model 36 x 25 that shows each of the four separate partial products. I must know how to do the computation 36x25 showing each of the four partial products separately, and indicate how each corresponds to the drawing that is required of the area model. Answered by Penny Nom. 





Linear models 
19991109 

From Helen Moreno: What is a linear model? Answered by Harley Weston. 

