Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$ 4,000
A=$7,148
r=9.4%=0.094
n=4
substitute the given values
[tex]7,148=4,000(1+\frac{0.094}{4})^{4t}[/tex][tex]\frac{7,148}{4,000}=(1.0235)^{4t}[/tex]apply log both sides
[tex]\log (\frac{7,148}{4,000})=4t\cdot\log (1.0235)^{}[/tex]