1/10 C_1 e^1/10 t/(1 + 10^-7 C_1 e^1/10t) times e^-1/10t/e^-1/10 t = 1/10 C_1/(e

Question

1/10 C_1 e^1/10 t/(1 + 10^-7 C_1 e^1/10t) times e^-1/10t/e^-1/10 t = 1/10 C_1/(e^-1/10t + 10^-7 C_1) Thus, the value of P(t) is, P(t) = 1/10 C_1/10^-7 C_1 + e^1/10t Use the initial condition P(0) = 5000 in (4), to get: P(0) = 5000 in (4), to get: P(0) = 1/10 C_1/10^-7 C_1 + e^-1/10 (0) 5000 = 1/10 C_1/10^-7 C_1 + 1 5000 times 10^-7 C_1 + 5000 = 1/10 C_1 C_1 (5 times 10^-4 - 0.1) = -5000 C_1 = 5000/(0.1 -5 times 10^-4) C_1 = 5000/(0.1 -5 times 10^-4) C_1 = 5000/(0.1 -0.0005) I did not know a step from the solution from the solution, I was wondering why C1*1/10 does not become C2 in the calculations. I thought if I multiply C with another constant it will create another C. Unless if I multiply it an independent or dependent variable

Explanation / Answer

well you can change it to C2 but in order to find the constant C1 when you will apply the given initial condition you will have to substitute C2=C1/10 eventually so that you can find C1.  Its your choice if you wanna change it but in the end you have to change it back so you can let it remain as it is.

I hope this makes it clear.

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