Question

For an exponential function of the form y = ab^x with a > 0, what values of b result in a decreasing function?

-values between 0 and 1
-values greater than 1
-values equal to 1
-values less than 0​

Answer 1

For an exponential function of the form y = ab^x, where a > 0, the value of b determines whether the function is increasing or decreasing.

If b > 1, then the function is increasing, because as x increases, the value of b^x also increases, causing y to increase.

If 0 < b < 1, then the function is decreasing, because as x increases, the value of b^x decreases, causing y to decrease.

If b = 1, then the function is constant, because b^x = 1 for all values of x.

Therefore, to find values of b that result in a decreasing function, we need to find values of b such that 0 < b < 1.