Question

The models below are based on data collected by the Bureau of Economic Analysis from 1990 to 1997 in the United States. Let \(t\) represent the number of years since 1990 . Total sales (in billions of dollars) of services: \(S=\frac{1055+23 t}{1-0.04 t}\) Total sales (in billions of dollars) of hotel services: \(H=\frac{46+0.7 t}{1-0.04 t}\) Total sales (in billions of dollars) of auto repair services: \(A=\frac{48-t}{1-0.06 t}\) Find the total sales given by each model in \(1990 .\)

Short answer

In 1990, the total sales (in billions of dollars) for the three sectors are \(S = 1055\), \(H = 46\), and \(A = 48\) respectively.

Step-by-step solution

Substitute \(t = 0\) into the function \(S\)

Substitute \(t = 0\) into the function \(S=\frac{1055+23 t}{1-0.04 t}\) which simplifies to \(S=1055\) as the fraction simplifies to \(1055/1\) when \(t = 0\).

Substitute \(t = 0\) into the function \(H\)

Substitute \(t = 0\) into the function \(H=\frac{46+0.7 t}{1-0.04 t}\) which simplifies to \(H=46\) as the fraction simplifies to \(46/1\) when \(t = 0\).

Substitute \(t = 0\) into the function \(A\)

Substitute \(t = 0\) into the function \(A=\frac{48-t}{1-0.06 t}\) which simplifies to \(A=48\) as the fraction simplifies to \(48/1\) when \(t = 0\).