1 State the asymptote for the function THERE IS AN ASYMPTOTE

1. State the asymptote for the function. THERE IS AN ASYMPTOTE.

a) y = 7 - e ^ x

b) -e ^ (x-1) - 3

2. When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient\'s bloodstream after t hours is modeled by:

D(t) = 40 e ^ (-0.4t)

where m(t) is measured in grams.

a) Find the mass at time t = 0

______ grams

b) How much of the mass remains after 4 days? (Round your answer to three decimal places)

_____ grams

Solution

1)

the function y=e^x , has an horizontal asymptote at

y=0

a) Horizontal Asymptote y=0

b) Horizontal Asymptote

As the function is shifted by 3 units downwards

So HA at y=-3

2)

D(t) 40 e^(-0.4t)

a) at t=0

D(t) = 40 e^(-0.4 *0)

= 40 e^0

=40 miligrams

= 0.04 grams

b) D(t) = 40 e ^ (-0.4* 4) = 40 * e^(-1.6) = 8.076 miligrams = 0.008 grams