$f\left(x\right)=\frac{1}{4}\cdot 2^x-3$: multiplication of $a\left(x\right)=2^x$ with 1/4 with respect to the $x$ -axis and a translation of $-3$ along the $y$ -axis
$g\left(x\right)=\frac{1}{2}\cdot {0.5}^x-1$: multiplication of $b\left(x\right)={\left(\frac{1}{2}\right)}^x$ with 1/2 with respect to the $x$ -axis and a translation of $-1$ along the $y$ -axis

$2^{x-2}=2^{-3}$ gives $x=-1$

${\left(\frac{1}{3}\right)}^{x-3}=\frac{5}{8}$ gives $x\approx 3.68$. Solution: $x<3.68$

$g\left(4\right)=1$. Graph: if $x\le 4$, then $g\left(x\right)\ge 1$.

Study the graphs: $-3<p\le -1$

$A=(-1,-2\frac{7}{8})$ and $B=(-1,63)$. So the length of $AB$ is $63--2\frac{7}{8}=65\frac{7}{8}$.

$C=(5,5)$ en $B\approx (\mathrm{2,415};5)$. Dus is $CD\approx 5-\mathrm{2,415}=\mathrm{2\; <mo>,</mo>585}$.

$x\approx 1.43$

$x\le 1.43$

$5^x=\frac{5}{3}$ gives $x\approx 0.32$

$x\ge 0.32$

$x\approx -0.63$

$x\le -0.63$

${\left(\frac{1}{3}\right)}^x=2$ gives $x\approx -0.63$

$x>-0.63$

$2^x=2^{1\frac{1}{2}}$ gives $x=1\frac{1}{2}$

$2^{2x}=2^{3(x+2)}$ gives $x=-6$

$3^{4x}=3^{\frac{1}{2}}$ gives $x=\frac{1}{8}$

$2^{2x-1}=2^5$ gives $x=3$

$2^{\frac{1}{2}x+1}=2^{2\frac{1}{2}}$ gives $x=3$

$2^{2x}=2^0$ gives $x=0$

$2^{3x^2}=2^{4x}$ gives $x=0\vee x=\frac{4}{3}$

$2^{\mathrm{-}x}=2^3$ gives $x=-3$

$2^{x+5}=2^2$ gives $x=-3$

$2^{5(3x-2)}=2^{-2}$ gives $x=\frac{8}{15}$

$x=3$

$p=4$

$t=2$

$x<4$

$x\le 1$

$x\le -4$

$x>2$

$x<2$

$x<0.17$

$x>1.5$

$x>-49$

$x\le 3$

$x<2.5$

$540\cdot {0.95}^t$ is decreasing, so $540-540\cdot {0.95}^t$ is increasing.

$A=540$

The medication enters the blood slower and slower.

Solving $405=540-540\cdot {0.95}^t$ gives $t\approx 27.03$, so just after $27$ minutes.