# Calc 2 college

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Modeling with differential equations.
If a bacteria culture doubles every 10 minutes and the original culture has 300 cells determine the rate of growth.

• Calc 2 college -

y = c e^kt

dy/dt = k c e^kt = k y

when t = 0 e^kt = e^0 = 1
y(0) = c

so
y = 300 e^kt
when t = 10
y = 600
600 = 300 e^10k
2 = e^10 k
ln 2 = 10 k
k = .0693/minute

• Calc 2 college -

Thanks

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