Answer:
[tex]h=2.4 hours \: 2hours\:24'[/tex]
Step-by-step explanation:
1)Rewriting it properly:
[tex]Q(t)=28850*\left ( \left ( \frac{3}{4}\right )^{h} \right )^{\frac{t}{h}}\, if \left ( \frac{3}{4} \right )^{h}=\frac{1}{2}[/tex]
2) Let's calculate the time (in hours), based on this relation:
[tex]\left ( \frac{3}{4} \right )^{h}=\frac{1}{2} \Rightarrow log_{\frac{3}{4}}\frac{1}{2} \Rightarrow h \approx 2.4\: hours[/tex]
3) Testing it. We must find something around the half of 28850, due to some rounding in logarithms.
[tex]Q(t)=28850*\left ( \left ( \frac{3}{4}\right )^{h} \right )^{\frac{t}{h}}\, if \left ( \frac{3}{4} \right )^{h}=\frac{1}{2}\Rightarrow h=\\Q(t)=28850(\frac{1}{2})^{\frac{t}{h}}\Rightarrow Q(t)=28850(\frac{1}{2})^{\frac{t}{2.4}}\\28850(\frac{1}{2})^{\frac{t}{2.4}}=14425 \Rightarrow (\frac{1}{2})^{\frac{t}{2.4}}=\frac{14425}{28850}\Rightarrow (\frac{1}{2})^{\frac{t}{2.4}}=\frac{1}{2}\Rightarrow t=2.4\\Q(2.4)=28850*\left ( \left ( \frac{3}{4}\right )^{2.4} \right )^{\frac{2.4}{2.4}}\Rightarrow Q\approx14464[/tex]
4) So, h≈ 2.40 hours or 2 hours 24'
