Math Insight

Gateway exam, version 4503

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Compute the value of $f(f(\frac{1}{ 5 }))$ for the function $f(x)=4x(1-x)$.

    $f(f(\frac{1}{ 5 })) =$

  2. Rewrite the exponential function \[ w(t) = \frac{ 76 }{ 6^{ t - 3 } } \] in the form $w(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:

    $a = $

    $b = $

  3. Let the variable $x$ be in the range \begin{align*} -1< x <4. \end{align*} If $y= 7 x + 1$, what is the range of the variable $y$?


    $\lt y \lt$

  4. Solve the equation $9\left(y + 1\right)^{2} \left(y + 3\right)^{2} \left(y + 10\right)^{2} \left(4 y - 2\right) =0$.

    The solutions are $y = $

    If there are more than one solution, separate answers by commas

  5. Simplify the inequality below: \begin{align*} \left|5 x - 7\right|<4 \end{align*}


    $\lt x \lt$

  6. Consider the function $f(t)=13(1.35)^t. \;\;$ Find the doubling time, i.e. find $t$ such that $f(t)= 2f(0).$

    Doubling time =

    (If you round your answer, include at least 4 significant digits.)

  7. Solve for $q$. \begin{align*} 10 q - 4 s - 10 = - 9 s + 6 \end{align*} $q = $

  8. Let $g(x) = - 9 e^{x - 5}$ and $z(x) = 5 x^{2} + x$. What is $g(z(x))$?

    $g(z(x)) = $

    Need help?

  9. Solve the equation $y^{2} - 3 y + 2 =0$ by factoring.

    The solutions are $y = $

    If there are more than one solution, separate answers by commas

  10. Find the equation for the line through the point $(0,0)$ with slope given by $m=\frac{16}{5}$

    $y = $