Thread: 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= One milligram raises the body temp 2.3* C. Find the function

Where do I start with this problem?



Thanks

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)

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?

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

the patient is long dead.

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