Question

Mrs. Eaton's class is participating in the "Box Tops for Education" campaign. On the first day, her

Answer 1

Each colection day: D
Number of tops collected on that day: N

D1=1; N1=2
D2=3; N2=8

1) Linear model
N-N1=m(D-D1)

m=(N2-N1)/(D2-D1)
m=(8-2)/(3-1)
m=(6)/(2)
m=3

N-N1=m(D-D1)
N-2=3(D-1)
N-2=3D-3
N-2+2=3D-3+2
N=3D-1

when D=6:
N=3(6)-1
N=18-1
N=17

What is the number of tops collected on the sixth day based on the linear model?
The number of tops collected on the sixth day based on the linear model is 17.

2) Exponential model
N=a(b)^D
D=D1=1→N=N1=2→2=a(b)^1→2=ab→ab=2   (1)

D=D2=3→N=N2=8→8=a(b)^3→8=a(b)^(1+2)
8=a(b)^1(b)^2→8=ab(b)^2   (2)

Replacing (1) in (2)
(2) 8=2(b)^2
Solving for b:
8/2=2(b)^2/2
4=(b)^2
sqrt(4)=sqrt( b)^2 )
2=b
b=2

Replacing b=2 in (1)
(1) ab=2
a(2)=2
Solving for a:
a(2)/2=2/2
a=1

Then, the exponential model is N=1(2)^D
N=(2)^D

When D=6:
N=(2)^6
N=64

What is the number of tops collected on the sixth day based on the exponential model?
The number of tops collected on the sixth day based on the exponential model is 64