Test Section09SettingUpFunctionsTest

If $g(x) = 3\sin(2x)$ and $x = 4\cos(2t)$, find a formula for the function $g(t)$.
$g(t) =$

Write a formula for $A$ in terms of $w$ if $A=lw$ and $2l+2w=100$.
$A(w) =$

The amount of material, $A$, that a student remembers $t$ hours after memorizing it is given as a function of time by $A(t) = (A_0 - A_1) + A_1 ({1\over2})^{t/h}$, where $A_0$ is the initial amount of material memorized, $A_1$ the amount the student will remember, and $h$ the half-life of material that is forgotten. Which of the following is true?

$P$ dollars are deposited in a bank account with a fixed annual interest rate, $r$, compounded continuously. After $t$ years, the balance in the account is $B = P e^{rt}$. Which of the following is true?

If $s = {1\over2}gt^2 + vt + h$, what is the coefficient of $t^2$?

If $B(t) = P_0(1 + {r\over12})^{12t}$, what is the coefficient of $r$?

Write a formula for the function $V(r)$ if $V={1\over3}\pi r^2h$ and ${r\over6}={h\over10}$.
$V(r) =$

If $y = \ln({x+4\over 5})$, what is the coefficient of $x$?

If $A=\pi r^2$ and $r = 3t^2$, write a formula for $A$ as a function of $t$.
$A(t) =$

In the decreasing exponential function $f(x)=a^{-x}$, which of the following is true?