#Exponential Growth Calculus

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silk hamlet
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Exponential Growth Calculus

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pseudo harbor
# silk hamlet Exponential Growth Calculus

rate = 3000e^(3t/5)
let A = initial number of bacteria, then the number of bacteria at time t is:
B(t) = A(1 + 3000e^(3t/5))
t = 0 -> B(t) = 7500
7500 = A(1 + 1)
7500 = 2A
A = 3750
B(t) = 3750(1 + 3000e^(3t/5))
B(5) = 3750(1 + 3000³)
B(5) = 3750(1 + 27 × 10⁹) = ...

silk hamlet
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@pseudo harbor

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im pretty sure we are supposed to sue derivatiaves

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so like

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so using smth like this

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@pseudo harbor

pseudo harbor
silk hamlet
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ye

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@pseudo harbor

pseudo harbor
# silk hamlet ye

dy = 3000e^(3t/5) dt
u = 3t/5
du = (3/5) dt
dt = (5/3) du
dy = 3000e^u * (5/3) du
dy = 5000e^u du
integrate both sides
y = 5000e^u + C
y = 5000e^(3t/5) + C
t = 0 -> y = 7500
7500 = 5000 + C
C = 2500
y = 5000e^(3t/5) + 2500
t = 5:
y = 5000e³ + 2500 = ...

silk hamlet
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so what do i do

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for the addiiton

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of the 7500

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@pseudo harbor

pseudo harbor
silk hamlet
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is 7500

pseudo harbor
silk hamlet
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ic co is this

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the final ans

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= 5000e³ + 2500

pseudo harbor
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yes

silk hamlet
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ight thx a lot