Answer:
0.0642 or 6.42%
Explanation:
The period 't' between the year when the coin was issued, 1794, and 1971 is:
[tex]t=1971-1794 \\t=177\ years[/tex]
If the coin had a value of $5 and after a period of t=177 years it was worth $305,000, the annual tax rate by which the coin appreciated is determined by:
[tex]305,000 = 5*(1+r)^{177}\\r=\sqrt[177]{61,000}-1\\r=0.0642=6.42\%[/tex]
The annual rate was 0.0642 or 6.42%.
