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Answer :
To find the value of b in the exponential function y = 3125(b)^x that contains the point (5,1), we substitute in the values and solve for b, yielding b = (1/3125)^(1/5), which simplifies to b = 1/5 or 0.2.
The student is asking for the value of b in the exponential function y = 3125(b)x given that the point (5,1) lies on its graph. By substituting x with 5 and y with 1, we can solve for b.
The equation with the given point becomes:
1 = 3125(b)^5
Now, divide both sides of the equation by 3125 to isolate b5:
b5 = 1 / 3125
To find b, we take the fifth root of both sides:
b = (1 / 3125)^1/5
If you calculate the fifth root of 1/3125, you get:
b = 1 / 5
So, the value of b is 0.2.
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