1. ## Drug Absorption

A drug is administered intravenously for pain. The function
f(t)=90 - 52 ln (1 + t), 0<t<4 gives the number of units of the drug in the body after t hours.

a. What was the initial number of units of the drug administered?
b. How much is present after 2 hours.
c. Draw the graph of f.

In part a, you substitute t for 0. So you have 90-52 ln (1 + 0). and i know that Ln1 aways = 0 . So 90-52n(1) = 90. i don't know just doesn't sound right to me for some reason. Then you plug in 2 for t. I have a feeing there's some set method for answering this kind of equation but it evades me.

2. Originally Posted by fezz349
A drug is administered intravenously for pain. The function
f(t)=90 - 52 ln (1 + t), 0<t<4 gives the number of units of the drug in the body after t hours.

a. What was the initial number of units of the drug administered?
b. How much is present after 2 hours.
c. Draw the graph of f.

In part a, you substitute t for 0. So you have 90-52 ln (1 + 0). and i know that Ln1 aways = 0 . So 90-52n(1) = 90. i don't know just doesn't sound right to me for some reason. Then you plug in 2 for t. I have a feeing there's some set method for answering this kind of equation but it evades me.
Your method is correct. Why would you doubt it?

3. fezz349, you are almost there;

f(t)=90 - 52 ln (1 + t), 0<t<4

a) for t = 0 hour,

f(0) = 90 - 52 ln(1 +0) = 90 - 0 = 90 units of drug present

b) for t = 2 hours;

f(2) = 90 - 52 ln(1 + 2)

= 90 - 52 ln 3

= 90 - 52(1.0986)

= 90 - 57.13

= 32.87 units of drug remaining

c) See below,

4. alright thanks guys, it just seemed a little too straightforward, i guess every question isn't trying to trick u