Chapter 8, Problem 30P

Measurements of the concentration, C, of a substance during a chemical reaction at different times t are shown in the table.

t(h)	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0	5.0	5.5	6.0
C(g/L)	1.7	3.1	5.7	9.1	6.4	3.7	2.8	1.6	0.8	0.7	0.6

(a) Suppose that the data can be modeled with an equation in the form:

$C(t)=\frac{1}{a_2{t}^2+a_{2}t+a_0}$

Determine the coefficients a₀, a₁, and a, such that the equation best fits the data. Use the equation to estimate the concentration at t =2 h.

Make a plot of the data points and the equation.

(b) Suppose that the data can be modeled with an equation in the form:

$C(t)=\frac{1}{a_3{t}^3+a_2{t}^2+a_{1}t+a_0}$

Determine the coefficients a₀, a₁, a₂, and a₃such that the equation best fits the data. Use the equation to estimate the concentration at t=2 h. Make a plot of the data points and the equation.