u 与 t 的平方成反比。

1. Find key features and points of the graph

For $u=\dfrac{2}{t^2}$, $t\neq 0$.

Since $t^2>0$, $u>0$ for all $t\neq 0$.

Some points are:
$t=1,\quad u=\frac{2}{1^2}=2$
$t=-1,\quad u=\frac{2}{(-1)^2}=2$
$t=2,\quad u=\frac{2}{2^2}=\frac12$
$t=-2,\quad u=\frac{2}{(-2)^2}=\frac12$

2. Sketch the correct shape with symmetry and asymptotes

Sketch two branches above the $t$-axis:

• one branch for $t>0$ and one branch for $t<0$,
• symmetric about the $u$-axis,
• the graph gets very large as $t$ approaches $0$,
• the graph approaches the $t$-axis as $|t|$ becomes large.

The graph does not touch either axis.

1. Find the new value of $u$ as a fraction of the original value when $t$ is tripled

Since $u \propto \dfrac{1}{t^2}$, let the original value be $u$.

When $t$ is tripled, $t$ becomes $3t$.

So the new value of $u$ is proportional to
$\dfrac{1}{(3t)^2}=\dfrac{1}{9t^2}.$
Hence the new value of $u$ is $\dfrac{1}{9}$ of the original value.

2. Calculate the percentage change in $u$

Percentage change
$=\dfrac{\text{new} - \text{original}}{\text{original}}\times 100\%$
$=\dfrac{\frac{1}{9}u-u}{u}\times 100\%$
$=\left(\dfrac{1}{9}-1\right)\times 100\%$
$=-\dfrac{8}{9}\times 100\%=-88.888\ldots\%.$
So $u$ decreases by $88.9\%$ to 3 significant figures.