Question

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

class collected 2 tops. On the third day, her class collected 8 tops. Let D represent each collection
day and N represent the number of tops collected on that day.
Based on the situation, John claims the number of tops collected can be modeled by an exponential
function. Riley disagrees and claims the number of tops can be modeled with a linear function. What
is the number of tops collected on the sixth day based on the exponential model? What is the
number of tops collected on the sixth day based on the linear model?

Answer 1

Explanation:

for the exponential it is actually 64

Answer 2

The exponential model would take the form:

`y=Ae^(kt)`
A, the initial value is 2, we will use 3 days and 8 tops to find k, or the rate.

`8 = 2e^(k*3)`

`k = (ln(4))/(3)`

Now, plugging in 6 days:

`y = 2e^{ (ln(4))/(3)*6}`

`y = 32`

The linear would take the form:
y = mx+b
First the slope would be: (8-2)/(3-1) = 3
And to find b we could plug in the point (8,3):
8 = 3(3)+b
b = 8-9
b = -1
y = 3x-1
At x=6
y = 3(6)-1
y = 17

Thus, the exponential is almost double the result of the linear! Hope that helps.