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## 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