consider the exponential equation y = Ca^t, where C and a are positive real constants and t is a positive real number

Question

consider the exponential equation y = Ca^t, where C and a are positive real constants and t is a positive real number. the value of y decreases as the value of t increases if and only if which of the following statements about a is true?

F. -1 < a

G. 0 <a

H. 0 < a < 1

J. 1 < a < 2

K. 1 < a

Answer 1

If a is a fraction, like 1/2 or 1/3, then raising it to a positive power results in a smaller number.

 

Let C = 1, let a = 1/2.

 

If t = 1, y = .5

If t = 2, y = .25

 

Etc.