Thus, the solution is (1,4) and that represents the number in which the number of visitors incoming when the temperature is increasing matches the number of visitors leaving early when the temperature is decreasing.
1) The solution to both functions is that point that is located at the intersection of the curve and the line.
2) So, let's solve this system of equations:
[tex]\begin{gathered} \begin{matrix}y=4^x\end{matrix} \\ y=-x+5 \\ \end{gathered}[/tex]Note that we can apply the Substitution Method:
[tex]\begin{gathered} 4^x=-x+5 \\ \ln4^x=\ln_(-x+5) \\ x\ln(4)=\ln_(-x+5) \\ x=\frac{\ln(-x+5)}{\ln(4)} \\ \frac{\ln \left(-x+5\right)}{\ln \left(4\right)}=x \\ \frac{\ln \left(-x+5\right)}{\ln \left(4\right)}\ln \left(4\right)=x\ln \left(4\right) \\ \ln \left(-x+5\right)=x\ln \left(4\right) \\ \ln \left(-x+5\right)=2\ln \left(2\right)x \\ e^{\ln \left(-x+5\right)}=e^{2\ln \left(2\right)x} \\ -x+5=4^x \\ -(1)+5=4^1 \\ 4=4 \\ x=1 \end{gathered}[/tex]With the quantity of x=1 we can plug it into the second formula:
3)
[tex]\begin{gathered} y=-x+5 \\ y=-1+5 \\ y=4 \end{gathered}[/tex]4) Thus, the solution is (1,4) and that represents the number in which the number of visitors incoming when the temperature is increasing matches the number of visitors leaving.
