Answer
a) See graph
b) $2453$ billion
c) In $1993$
d) In $1999$
e) In $1939$ and $1975$
f) $[2453, 6125]$
Work Step by Step
Given $$\begin{aligned}
D(t) &= 17(t-3)^2 +2300.
\end{aligned}$$ a) The graph of the function is shown below.
b) Determine $D(t)$ for $t=6$: $$\begin{aligned}
D(6) &= 17(6-3)^2 +2300\\
&= 2453.
\end{aligned}$$ This suggests that in $1996$, households and non-profit organizations invested about $2453$ billions in time and saving accounts.
c) When $t= 3$, the function $D(t)$ has its minimum value of $2300$. This means that in about $1993$ the minimum value of time and saving account was about $2300$ billion.
d) The graph shows that at $t= 9$, $D(t)\approx 3000$. Therefore, the time when households and nonprofit organizations investment in time and saving account reached 3000 billion was in $1999$.
e) Compute $D(t)$ for $t= 0$ and $t= 18$ to find the range of the function.
$$\begin{aligned}
D(0) &= 17(0-3)^2 +2300\\
& = 2453\\
D(18)& = 17(18-3)+2300\\
&= 6125.
\end{aligned}$$ The range of the function is $[2453, 6125]$.
