which statements are true about exponential decay functions? check all that apply. the domain is all real…

which statements are true about exponential decay functions? check all that apply. the domain is all real numbers. as the input increases, the output increases. the graph is the same as that of an exponential growth function. the base must be less than 1 and greater than 0. the function has a constant multiplicative rate of change.

which statements are true about exponential decay functions? check all that apply. the domain is all real numbers. as the input increases, the output increases. the graph is the same as that of an exponential growth function. the base must be less than 1 and greater than 0. the function has a constant multiplicative rate of change.

Answer

Brief Explanations:

  • For an exponential decay function of the form $y = a\cdot b^x$ ($a>0$, $0 < b<1$), the domain is all real - numbers since we can substitute any real number for $x$.
  • In an exponential decay function, as the input $x$ increases, the output $y$ decreases because the base $b$ is between 0 and 1.
  • The graph of an exponential decay function is different from that of an exponential growth function. Exponential growth has $b > 1$ and decay has $0 < b<1$.
  • The base $b$ of an exponential decay function must satisfy $0 < b<1$.
  • An exponential function (both growth and decay) has a constant multiplicative rate of change. Each time $x$ is incremented by 1, the output is multiplied by the base $b$.

Answer:

The domain is all real numbers. The base must be less than 1 and greater than 0. The function has a constant multiplicative rate of change.