Geometry Word Problem

Question

Use the info provided to answer part A and part B.

During the 1st day of a canned-goods drive, Jasmine's home room teacher collected 2 cans. During the 3rd day the teacher collected 8 cans. Let D represent each collection day, and let N represent the number of canned goods collected on that day.

 

Part A 

Based on the situation, Jasmine claims that the number of canned goods collected can be modeled by an exponential function. What is the number of canned goods collected on the 6th day based on an exponential model?

 

Part B

Ramon disagrees with Jasmine and claims that the number of canned goods collected can be modeled by a linear function. Which statement is true about the number of cans predicted to be collected on the 6th day based on the two models?

Answer 1

When D = 1, N = 2

When D = 3, N = 8

 

A.  As an exponential function:  N = 2^D

     Given D = 6, N = 2⁶ = 64 cans collected on day 6

 

B.  As a linear function we have 2 points (d,n):

     (1, 2), (3, 8)

     Slope m = (8-2)/(3-1) = 6/2 = 3

 

    y = mx + b

    Since we are using points (d, n) instead of (x, y)

    n = 3d + b

    Using (1,2) solve for b

    2 = 3(1) + b

    b = -1

    n = 3d -1

 

On day 6 in the linear model:  n = 3(6)-1 = 17 cans collected

 

Without further points to test we can't say for 100% certain which

model is correct;  however, I would definitely lean toward the

linear equation given the extreme rate at which the exponential

function will rise.