#### Answer

The linear function in slope-intercept form that models the total spending, $p\left( x \right)$, by Americans x years after $1950$ is $p\left( x \right)=0.22x+3$.

#### Work Step by Step

From the provided information, the rate of change of the increase in the budget is provided as $0.22\%$. This represents the slope with a positive sign.
$m=0.22$.
And the value of c is provided as $22\%$ because the Americans spent $3\%$ of their budget in $1950$ (which is the starting year that shows the y intercept).
Substitute the values $m=0.22$ and $c=3$.
The obtained linear model is:
$p\left( x \right)=0.22x+3$