s(t) = 57 1 + 0.5e−0.8t

Question

As t decreases without bound, the output values of s  ---Select--- approach zero increase without bound decrease without bound approach a limiting value of 57 . 

As t increases without bound, the output values of s  ---Select--- approach zero increase without bound approach a limiting value of 57 decrease without bound .

(b) Write limit notation for the end behavior. 

lim t → −∞ s(t)	=
lim t → ∞ s(t)	=

 

(c) Write the equations for any horizontal asymptote(s). (If an answer does not exist, enter DNE.) 

y =	(smaller value)
y =	(larger value)

Answer 1

As t decreases without bound, the exponent increases and s increases without bound.

As t increases without bound 0.5e^(-0.8t) gets smaller and approaches zero. If the expression is supposed to read 57*(1+0.5e^(-0.8t)) then it approaches the limiting value of 57.

(b) ∞  and 57

(c) y=57 (smaller value), y=DNE (larger value)