a) Solve $e^x=9$. Write your answer correct to 2 decimal places,
b) Differentiate $y=x e^x$

c) Find the equation of the tangent to the curve $y=1+\ln (2 x)$ at $x=1$.
d)

The diagram above shows part of the graph of $y=\frac{2}{x-2}+2$.
The curve intersects the $x$-axis at $x=1$.
Find the exact value of the shaded area.

a) Write $72^{\circ}$ in radians in terms of $\pi$
b) Solve $3 \tan ^2 x=1$ for $0 \leq x \leq 2 \pi$
c) Solve $\log _2(x)=1+\log _2(x-1)$
d) A company manufacturing electrical components finds that the cost (in \$) of $\quad 2$ producing $x$ components per month is given by $C(x)=72000+60 x$

Find the marginal average cost at a production level of 300 components per month and interpret the result.

A company produces $x$ pillows per week. The cost equation is $C(x)=200-40 x$ and revenue is given by $R(x)=600 x-2 x^2$. Which of the following gives the profit?
$P(x)=200-2 x^2-640 x$
$P(x)=560 x-2 x^2-200$
$P(x)=640 x-2 x^2-200$
$P(x)=2 x^2-640 x+200$

Which of the following best shows the solution of $3^x<0.5$ ? $x>-1.585$
$x<-1.585$ $x>-0.631$
$x<-0.631$

The share price $(\$ P)$ of a renewable energy company is increasing such that $\frac{d P}{d t}=\frac{6}{e^t}$, where $t$ is the time in months since the listing of the company. The initial price of the shares is $\$ 2$. Which of the following is closest to the share price after 3 months?
$\$ 8.30$
$\$ 2.30$
$\$ 7.70$
$\$ 18.00$