we have the function
[tex]f(x)=1,822.8(1.4)^x[/tex]
when
f(x)=406,500,000,000
Find out the value of x
substitute the given value in the function
[tex]\begin{gathered} 406,500,000,000=1,822.8(1.4)^x \\ \frac{406,500,000,000}{1,822.8}=1.4^x \end{gathered}[/tex]
Apply log on both sides
[tex]\begin{gathered} log\frac{406,500,000,000}{1,822.8}=log1.4^x \\ \\ log\frac{406,500,000,000}{1,822.8}=(x)log1.4 \\ \\ x=\frac{log\frac{406,500,000,000}{1,822.8}}{log1.4} \\ \\ x=57.13 \end{gathered}[/tex]
therefore
The answer is x=57
