ANSWER
t = 10.27
EXPLANATION
Step 1: Given
[tex]500e^{0.0675t}\text{ = 1000}[/tex]
Step 2: Divide both sides by 500
[tex]\begin{gathered} \frac{500e^{0.0675t}}{500}\text{ = }\frac{1000}{500} \\ e^{0.0675t}\text{ = }2 \end{gathered}[/tex]
Step 3: Take the natural logarithm of both sides
[tex]\begin{gathered} 0.0675t\text{ = ln 2} \\ 0.0675t\text{ = }0.69314718056 \end{gathered}[/tex]
Step 4: Divide both sides by 0.0675
[tex]\begin{gathered} \frac{0.0675t}{0.0675}\text{ = }\frac{0.69314718056}{0.0675} \\ t\text{ = 10.268847} \end{gathered}[/tex]
Hence, t = 10.27 (rounded to the nearest hundredth).
