Answer
$
T= 24071+602.3t
$
$
T(t)=24071(1.02258)^t
$
Work Step by Step
A)
Take $t= 0$ for 2003 so that $t= 10$ corresponds to the 2013.
Let $T= b+mt$, then $T= 24071+m\cdot0 = 24071=b$. We find the slope from:
$$
m=\frac{\Delta T}{\Delta t}=\frac{30094-24071}{10-0}=602.3
$$
The required formula is
$$
T= 24071+602.3t
$$
B)
Let $T(t)=a(b)^t $ for the exponential function of tuition growth in the US. The value of $a$ can be taken directly from problem as $a= 24071$. We now have $N(t)= 24071(b)^t$. Use the point (10,30094) to find the value of $b$.
$$
\begin{aligned}
24071(b)^{10}& =30094 \\
b^{10} & =\frac{30094}{24071}=1.2502\\
b & =(1.2502)^{1 / 10}=1.02258
\end{aligned}
$$
The required formula is
$$
T(t)=24071(1.02258)^t
$$
