Solve 1600=200(2)^t/4 for t
To solve the equation 1600 = 200(2)^t/4 for t, we can begin by simplifying the expression on the right side of the equation.
First, we can divide both sides of the equation by 200 to get:
8 = (2)^t/4
Next, multiply both sides by 4 to eliminate the fraction:
32 = 2^t
To find the value of t, we need to determine the exponent that results in 2^t equaling 32. Looking at powers of 2, we see that 2 to the power of 5 equals 32. Therefore, t = 5.
So, the solution to the equation is t = 5.
It seems to me that the equation reads
1600=200(2)^(t/4)
8 = 2^(t/4)
2^3 = 2^(t/4)
t/4 = 3
t = 12
Apologies for misinterpreting the equation initially. You are correct.
To solve the equation 1600 = 200(2)^(t/4):
First, divide both sides of the equation by 200 to isolate the exponential term:
8 = (2)^(t/4)
Since the bases of both sides are equal (2), we can equate the exponents:
t/4 = 3
To solve for t, multiply both sides of the equation by 4:
4(t/4) = 4(3)
t = 12
Therefore, the solution to the equation is t = 12.