High School

An exponential function in the form \( y = 3125(b)^x \) contains the point \((5, 1)\). What is the value of \( b \)?

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.