Gateway exam practice - Math Insight

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Total points: 10

Time limit: 50 minutes

Solve the equation $z^{2} + z - 2 =0$ by factoring.
The solutions are $z = $

If there are more than one solution, separate answers by commas
Let $u(x) = e^{2 x - 2}$ and $k(x) = - 8 x^{2} + x$. What is $u(k(x))$?
$u(k(x)) = $

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Hint
Use ^ to enter an exponent, e.g., for $a^b$, type a^b.
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Consider the function $f(t)=6(1.55)^t. \;\;$ 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.)
Write the function $f(x)=24e^{ 2x+4 }$ in the form $f(x)=Ae^{kx}$. What are the values of the parameters $A$ and $k$?
$A=$
, $k=$

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Hint
Use ^ to enter an exponent, e.g., for $a^b$, type a^b.
Hide help
Let the variable $x$ be in the range \begin{align*} 1< x <7. \end{align*} If $y= 4 x + 4$, what is the range of the variable $y$?

$\lt y \lt$
Simplify the inequality below: \begin{align*} 1<\frac{8 x}{3} - 1<3 \end{align*}

$\lt x \lt$
Solve the equation $-5\left(x + 4\right) \left(x + 6\right) \left(x + 10\right)^{2} \left(6 x - 2\right) =0$.
The solutions are $x = $

If there are more than one solution, separate answers by commas
Find the equation for the line through the point $(-7,6)$ with slope given by $m=- \frac{2}{9}$
$y = $
Solve for y. \begin{align*} 10 y - 8 = - 6 y - 7 \end{align*} $y = $
Compute the value of $f(f(\frac{1}{ 5 }))$ for the function $f(x)=2x(1-x)$.
$f(f(\frac{1}{ 5 })) =$