# Can I get help on a rate of change problem?

• Aug 3rd 2009, 12:58 PM
Darkhrse99
Can I get help on a rate of change problem?
The rate of change in a person's body temp, with respect to the dosage of X milligrams of a drug, is given by D Prime of x= $\frac{7}{x+5}$ One milligram raises the body temp 2.3* C. Find the function

Thanks
• Aug 3rd 2009, 01:31 PM
Calculus26
D ' (x) = 7/(x+5)

D(x) = 7ln(x+5) + C

taking the normal body temp to be 37.5 (Centigrade) then D(1) = 39.8

D(1) = 7ln(6) + C = 39.8 which yields C= 39.8 - 7ln(6)

D(x) = 7ln(x+5) + 39.8 - 7ln(6)
• Aug 3rd 2009, 01:56 PM
Darkhrse99
Is the answer D(x)= 7ln|x+5|+2.3, or D(x)= 7ln|x+5|-10.2?

Those are the 2 multiple choose answers that are given with this problem?
• Aug 3rd 2009, 03:37 PM
Calculus26
If D(x) represents the persons body temperature neither one is right

as D(0) = 13.6 deg in one case and 1 deg in the other--in either case

If D(x) represents the temp above normal body temp

D(x) = 7ln(x+5) + C

D(1) = 7ln(6) +C = 2.3

in which case C = -10.2

D(x) = 7ln(x+5) - 10.2