Answer:
t= 12
Explanation:
Given the equation:
[tex]1600=200(2)^{\frac{t}{4}}[/tex]Step 1: Isolate the term containing t by dividing both sides by 200.
[tex]\begin{gathered} \frac{1600}{200}=\frac{200(2)^{\frac{t}{4}}}{200} \\ 8=(2)^{\frac{t}{4}} \end{gathered}[/tex]Step 2: Express 8 as a power of 2
[tex]2^3=2^{\frac{t}{4}}[/tex]Step 3: Cancel equal bases on both sides (in this case 2)
[tex]\begin{gathered} 3=\frac{t}{4} \\ t=3\times4 \\ t=12 \end{gathered}[/tex]The value of t is 12.
