Answer
a) $[9075,36900]$;
b) $\$2546.25$
c) Independent: $x$; dependent: $T$
d) See graph
e) $\$27,500$
Work Step by Step
We are given the function:
$T(x)=0.15(x-9075)+907.50$
As $x$ is between 9075 and 36,900, the domain of the function $T$ is:
$[9075,36900]$
b) Determine $T(20,000)$:
$T(20,000)=0.15(20,000-9075)+907.50=2546.25$
c) The independent variable is $x$, while $T$ is dependent on $x$.
d) Compute $T(9075)$ and $T(36900)$:
$T(9075)=0.15(9075-9075)+907.50=907.50$
$T(36,900)=0.15(36,900-9075)+907.50=5081.25$
Graph the linear function $T$ on the domain $[9075,36900]$, using the points $(9075,907.50)$ and $(36900,5081.25)$.
e) Solve the equation $T(x)=3671.25$:
$0.15(x-9075)+907.50=3671.25$
$0.15(x-9075)+907.50-907.50=3671.25-907.50$
$0.15(x-9075)=2763.75$
$x-9075=\dfrac{2763.75}{0.15}$
$x-9075=18,425$
$x-9075+9075=18,425+9075$
$x=27,500$
