Final answer:
To find the equation for an exponential function that passes through the points (1, 1.6) and (2, 0.32), we can use the general form of an exponential function, y = a * b^x. By substituting the values of the points into the equation and solving for the constants a and b, we find that the equation becomes y = 8 * 0.2^x.
Step-by-step explanation:
To find the equation for an exponential function that passes through the points (1, 1.6) and (2, 0.32), we can use the general form of an exponential function, which is y = a * b^x, where a and b are constants. We can substitute the x and y values of both points into the equation to create a system of two equations. Solving this system of equations will give us the values of a and b, which we can then use to write the equation for the exponential function.
Substituting the values of (1, 1.6) into the equation, we get: 1.6 = a * b^1
Substituting the values of (2, 0.32) into the equation, we get: 0.32 = a * b^2
By dividing the second equation by the first equation, we can eliminate the variable a and solve for b: 0.32/1.6 = b^2/b^1 = b
Therefore, b = 0.2. Substituting this value into the first equation, we can solve for a: 1.6 = a * 0.2^1. Simplifying, we get a = 8.
Therefore, the equation for the exponential function is y = 8 * 0.2^x.