QUESTION $6[5]$

$6\mathrm{.}1$ Use Newton's method to approximate the solution of: $x^3=4x^2-1$ given $x_1=0\mathrm{.}5,($correct to $3$ decimal places$).$

OUESTION $7[6]$

$7\mathrm{.}1$ The velocity of a chemical reaction is given by $\frac{dx}{dt}=k(a-x),$ where $x$ is the amount transferred in time $t,k$ is a constant and $a$ is the concentration at time $t=0$ and when $x=0.$ Solve the differential equation and determine $x$ in terms of $t.$

$(6)$