- #1
Deathfish
- 86
- 0
Homework Statement
A biomedical company finds that a certain bacteria used for crop insect control will grow exponentially at the rate of 12% per hour. Starting with 1000 bacteria, how many will they have after 10h?
Homework Equations
Topic is application of differential equations.
y=Ce^kt
The Attempt at a Solution
This question is from the topic on application of differential equations.
I stumbled on the solution but i need to understand why it works and whether it is the correct method.
y+dy/dt=Ce^(0.12t)
at T=0, y=1000, dy/dt=0
1000+0=Ce^(0.12*0)
C=1000
Total T=y+dy/dt
T=1000e^(0.12t)
from here i just substitute in t=10 to get answer.
question is why exponential growth in this case uses base e and not other base? why does it work when C is initial value?
also is this the correct method when using differential equations to solve this problem? don't want the working to be affected just cause I know the formula is y=Ce^kt