Which function represents exponential decay?

Question

1) 2^0.3t

2) 1.2^3t

3) (1/2)^-t

4) y=5^-t

 

please explain how it is 4 I would think it was 3

Answer 1

Exponential decay requires a negative exponent (variable) and a constant base > 1.

 

#3 can be simplified as 2^t so that's exponential growth.  #4 is the answer.

Answer 2

So, Nat, remember that a negative exponent flips your fraction upside down. (1/2)^-t = 2^t.  (1/2)^-1 = 2¹ = 2. As t grows, it's going to increase (1/2)^-t. (1/2)^-2 = 2² = 4, and so on.

 

5^-t  = (1/5)^t, so as t grows, your fraction gets smaller. 5^-1 = (1/5)¹ = 1/5, but 5^-2 = (1/5)² = 1/25, and so on.

 

Hope this helps!