Question

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

Answer 1

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.