Linty Fresh
Junior Member
- Joined
- Sep 6, 2005
- Messages
- 58
The rate of healing for a skin wound in square centimeters per day is approximated by A'(t)=-0.9e^0.1t. If the initial wound has an area of 9 square centimeters, what will its area A(t) be after t days? After 5 days?
OK, so I start out with the derivative and try to find the integral:
A'(t)=-0.9e^0.1t
A(t)=-0.9 Integral e^0.1t dt
multiply the integrand by 0.1/0.1
A(t)=-9 Integral e^0.1t 0.1 dt
= -9 Integral e^u du
=-9e^0.1t + C
which strikes me as wrong. How can the area be negative? Did I mess up my math somewhere?
Many thanks!
On edit: Never mind. I just realized that C=18 and the actual equation for the area should be
A(t)=-9e^0.1t+18 Sorry about that!
OK, so I start out with the derivative and try to find the integral:
A'(t)=-0.9e^0.1t
A(t)=-0.9 Integral e^0.1t dt
multiply the integrand by 0.1/0.1
A(t)=-9 Integral e^0.1t 0.1 dt
= -9 Integral e^u du
=-9e^0.1t + C
which strikes me as wrong. How can the area be negative? Did I mess up my math somewhere?
Many thanks!
On edit: Never mind. I just realized that C=18 and the actual equation for the area should be
A(t)=-9e^0.1t+18 Sorry about that!