ABSTRACT
X(t) = X(0) + kt
X(t) → ∞ as t → ∞, but the limited amount of space and food in the bottle contradicts this. Hence, the model is not valid for large values of t.
To describe the best fit the vertical distance between the line and each data point must all be positive, otherwise errors cancel out. Use absolute values or squares of the differences. The best fit (for squares) is X ( t ) = 530 3 + 102 t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203746790/faf08795-153d-4b73-abf4-2726f3481269/content/eq998.tif"/>
(and once you have read §2.2 you will know how I know this!) At any rate, the fit is not satisfactory, since the data points clearly show that the graph of X(t) should bend downwards.
X(t) = (1 + a) t X(0
Interpretation: Again X(t) → ∞ t → ∞, since a > 0, so that the model is not valid for large values of t.
Validation: The best fit (for squares) is
X(t) = 209(1.288) t
which is unsatisfactory, since X(5) = 740.
Go, man, go!
