0,02e0,5t+0,5-0,02e0,5t = 1,5

Question

Aufgabe:

0,02e^0,5t+0,5-0,02e^0,5t = 1,5

Problem/Ansatz:

Wie löse ich die Gleichung auf? Bitte mit Rechenschritte!

Danke!

Answer 1

0.02·e^(0.5·t + 0.5) - 0.02·e^(0.5·t) = 1.5

0.02·√e·e^(0.5·t) - 0.02·e^(0.5·t) = 1.5

(0.02·√e - 0.02)·e^(0.5·t) = 1.5

e^(0.5·t) = 1.5 / (0.02·√e - 0.02)

0.5·t = LN(1.5 / (0.02·√e - 0.02))

t = 2·LN(1.5 / (0.02·√e - 0.02))

t = 9.500480486

Answer 2

\(0,02*e^{0,5t+0,5}-0,02e^{0,5t} = 1,5|*50\)

\(e^{0,5t+0,5}-e^{0,5t} =75\)

\(e^{0,5}*e^{0,5t}-e^{0,5t} =75\)

\(e^{0,5t}*(e^{0,5}-1) =75\)

\(e^{0,5t} =\frac{75}{(e^{0,5}-1)}\)

\(0,5t*lne =ln( \frac{75}{e^{0,5}-1}  )\)        \(ln e =1\)

\(0,5t =ln( \frac{75}{e^{0,5}-1}  )\)

\(t =2*ln( \frac{75}{e^{0,5}-1}  )\)