The graph of an exponential function passes through the points (–1,10) and 1,25. Write an equation for the function in the form y=a(b)x.y=

To find the equation of the exponential function in the form y = a(b)^x, we need to find the values of a and b.

We know that the function passes through the points (-1,10) and (1,25). We can substitute these points into the equation to get two equations and solve for a and b.

Substituting the point (-1,10) into the equation gives us:

10 = a(b)^-1

This simplifies to:

10 = a/b

Substituting the point (1,25) into the equation gives us:

25 = a(b)^1

This simplifies to:

25 = ab

Now we have a system of two equations:

10 = a/b

25 = ab

We can solve this system of equations to find the values of a and b.

First, multiply the two equations together to eliminate a:

10 * 25 = (a/b) * (ab)

250 = a^2

Taking the square root of both sides gives:

a = sqrt(250) = 15.81 (approx)

Substitute a = 15.81 into the equation 10 = a/b to find b:

10 = 15.81 / b

b = 15.81 / 10 = 1.581 (approx)

So, the equation of the exponential function is:

y = 15.81(1.581)^x