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

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

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

Answer

Brief Explanations:

  • For an exponential decay function (y = a\cdot b^{x}) ((a>0)), the domain is all real numbers because (x) can take any real - valued input.
  • The general form of an exponential decay function is (y=a\cdot b^{x}), where (0 < b<1). As (x) (input) increases, (b^{x}) gets smaller (since (0 < b<1)), so (y) (output) decreases. The statement "As the input increases, the output increases" is false.
  • The graph of an exponential decay function (y = a\cdot b^{x}(0 < b<1,a>0)) is decreasing, while the graph of an exponential growth function (y=a\cdot c^{x}(c > 1,a>0)) is increasing. So, the statement "The graph is the same as that of an exponential growth function" is false.
  • The base (b) of an exponential decay function (y=a\cdot b^{x}(a>0)) must satisfy (0 < b<1).
  • The general form of an exponential function (decay or growth) is (y=a\cdot b^{x}). The ratio of (y(x + 1)) to (y(x)) is (\frac{y(x + 1)}{y(x)}=\frac{a\cdot b^{x+1}}{a\cdot b^{x}}=b) (a constant). So, the function has a constant multiplicative rate of change.

Answer:

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