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Solve 1600 = 200(2)^(t/4) for t O t= 16 O t= 12 Ot =4 Ot=8

1 Answer

2 votes

Answer:

t= 12

Step-by-step explanation:

Given the equation:


1600=200(2)^{(t)/(4)}

Step 1: Isolate the term containing t by dividing both sides by 200.


\begin{gathered} (1600)/(200)=\frac{200(2)^{(t)/(4)}}{200} \\ 8=(2)^{(t)/(4)} \end{gathered}

Step 2: Express 8 as a power of 2


2^3=2^{(t)/(4)}

Step 3: Cancel equal bases on both sides (in this case 2)


\begin{gathered} 3=(t)/(4) \\ t=3*4 \\ t=12 \end{gathered}

The value of t is 12.

User Tim Gage
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