Substitution and Model Classification
Financial Modelling
Mr Maiku
Applied Function Modelling
Graphs
100
Substitute x=4x=4 into y=3x+7y=3x+7.
y = 19
100
Your savings follow M=200+50w, where w is the number of weeks. How much will you have after 4 weeks?
$400
100
How do you spell my first name?
Reginald
100
A cyclist’s distance is modelled by d=18t, where d is kilometres and t is hours. How far do they travel in 3 hours?
54km
100
State the vertex:
(2, 3)
200
Is y=5x2+2x+8 linear or quadratic? Explain how you know.
Quadratic: the highest power of x is 2.
200
A sponsorship follows M=6000+1800t. What do the numbers 6000 and 1800 represent?
$6000 initially, then an increase of $1800 each year.
200
What day of the week was I born on?
Thursday
200
A water tank initially contains 120 litres and fills at 15 litres per minute. Write a linear model for its volume, V, after t minutes.
V = 120 + 15t
200
State the 2 coordinates for this parabola's x intersections.
(2, 0) & (4, 0)
300
Substitute x=−3 into y=2x2+5
y = 23
300
A sponsorship follows M=5000+400t2. Calculate the total money received after 3 years.
$8600
300
How old was I when I got this chain?
1 day old
300
A ball’s height is modelled by h=-t2+6t, where h is metres and t is seconds. Find its height after 2 seconds.
8m
300
What is the maximum y value and at which x value does it occur?
y = 16
x = 4
400
Model A is y=4x+10. Model B is y=x2+10. Classify each model and determine which produces the greater value when x=5
A: linear; B: quadratic. A gives 30; B gives 35. B is greater by 5.
400
Sponsor A offers M=4000+2000t. Sponsor B offers M=4000+500t2. Which provides more money after 5 years, and by how much?
A: $14000
B: $16500
Sponsor B provides $2500 more
400
What colour was my first car?
Blue
400
A rectangular garden has width x metres and length x+4 metres. Write an expanded model for its area, classify the model, and calculate the area when x=6
A=x2+4x, a quadratic model. When x=6, A=60 m2.
400
State the 2 points where these lines intersect:
(1,5) and (5,5)
500
For equally spaced x-values of 0, 1, 2, 3 and 4, the corresponding y-values are 5, 8, 13, 20 and 29. Does a linear or quadratic model fit this pattern? Justify your answer using differences.
Quadratic. First differences: 3, 5, 7, 9. Second differences: 2, 2, 2, which are constant.
500
Sponsor A offers M=3000+1800t. Sponsor B offers M=3000+600t2. A manager says, “A pays more after one year, so it must also pay more after five years.” Test the claim and recommend a sponsor for a five-year contract based on total money received.
At 1 year: A = $4800; B = $3600. At 5 years: A = $12,000; B = $18,000. The claim is incorrect. Recommend B, which provides $6000 more after five years.
500
What size feet do I have?
10
500
Two machines fill water tanks. Their models are VA=20+12t and VB=20+3t2, where volume is in litres and time is in minutes. Apart from t=0, when do they contain the same volume, and which contains more after 5 minutes?
Equal at 4 minutes, with 68 L each. At 5 minutes: A = 80 L; B = 95 L. B contains 15 L more.
500
State the intersecting points of these lines.
(0, 3) & (5, 8)