Question

the height of a sand dune is represented by $f(t)=900 - 6t^{2}$ cm, where $t$ is measured in years since 1995. determine $f(12)$ and $f(12)$. (include units in each answer. note that you should enter year(s) as yr.) $f(12)=$ $f(12)=$

Explanation:

Step1: Calculate $f(12)$

Substitute $t = 12$ into $f(t)=900 - 6t^{2}$.
$f(12)=900-6\times12^{2}=900 - 6\times144=900 - 864 = 36$ cm.

Step2: Find the derivative of $f(t)$

Using the power - rule, if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. For $f(t)=900 - 6t^{2}$, $f^\prime(t)=0-12t=-12t$.

Step3: Calculate $f^\prime(12)$

Substitute $t = 12$ into $f^\prime(t)$.
$f^\prime(12)=-12\times12=-144$ cm/yr.

Answer:

$f(12)=36$ cm
$f^\prime(12)=-144$ cm/yr