Question

the total yearly amount of child support due (in billions of dollars) in the united states can be approximated by

d(t)=0.924t + 4.621

where t is the number of years since the study began, and d(t) is the amount due (in billions of dollars).

part 1 of 2

(a) evaluate d(0), d(4), and d(8).

d(0)=4.621

d(4)=8.317

d(8)=12.013

part: 1 / 2

part 2 of 2

(b) interpret the meaning of the function value of d(8).

d(8)=12.013 means that 8 year(s) since the study began, billion was due in child support in the united states.

Explanation:

Step1: Substitute \(t = 0\) into \(D(t)\)

\(D(0)=0.924\times0 + 4.621=4.621\)

Step2: Substitute \(t = 4\) into \(D(t)\)

\(D(4)=0.924\times4+4.621 = 3.696+4.621=8.317\)

Step3: Substitute \(t = 8\) into \(D(t)\)

\(D(8)=0.924\times8 + 4.621=7.392+4.621 = 12.013\)

Since \(D(t)\) represents the total yearly amount of child - support due (in billions of dollars) and \(t\) is the number of years since the study began. When \(t = 8\), we substitute into the function \(D(t)=0.924t + 4.621\) to get \(D(8)\). The value of \(D(8)\) gives the amount of child - support due at \(t = 8\) years.

Answer:

\(D(0) = 4.621\), \(D(4)=8.317\), \(D(8)=12.013\)

For part (b):