# Thread: Exponential and Logarithmic help!

1. ## Exponential and Logarithmic help!

I've done some of it but need some help on 2 parts..

Jane took 100mg of a drug in the morning and another 100mg of the same drug at the same time the following morning. The total amount of the drug in her body "t" days after the FIRST dosage was taken is given by

A(t) = 100e^-1.4t if 0≤t<1

A(t) = 100(1+e^1.4)e^-1.4t if t≥1

a) What was the amount of drug in Jane's body immediately after taking the second dose?

A(1) + A(0) = 100e^-1.4(1) + 100e^-1.4(0) = 124.66 mg

b) After 2 days?

A(2) = 100(1+e^1.4)e^-1.4(2) = 30.74 mg

c) In the long run?

(How do i do this one? I know it would eventually be 0)

d) Sketch the graph

(Sorta need help on this too)

Thanks!

2. Originally Posted by lilwayne

c) In the long run?

(How do i do this one? I know it would eventually be 0)
Try $\displaystyle t \to \infty$ for $\displaystyle A(t) = 100(1+e^{1.4})e^{-1.4t}$

$\displaystyle A(\infty) = 100(1+e^{1.4})e^{-1.4\infty} =100(1+e^{1.4})\times 0 = 0$