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Exponential growth (1 Viewer)
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ExtremelyBoredUser
Bored Uni Student
a. I = ie^-Rt/L. where i is initial
dI/dT =R/L * ie^-Rt/L
= R/L * I (I is the first equation)
dI/dT = RI/L
Therefore L * dI/dT = -IR and hence I = ie^-Rt/L is a solution as required.
b.
Parameters:
R=2 and T = 1/4, I = i/e (as shown in the book)
Substitution;
i/e = i * e^-2(1/4)/L
1/e = e^-2L/4, cancelled out the initial temperatures.
e = e^2L/4, took reciprocal
ln(e) = ln(e^2L/4) = 2L/4ln(e) , log laws
1 = 2L/4
2L = 4
Therefore L = 1/2
dI/dT =R/L * ie^-Rt/L
= R/L * I (I is the first equation)
dI/dT = RI/L
Therefore L * dI/dT = -IR and hence I = ie^-Rt/L is a solution as required.
b.
Parameters:
R=2 and T = 1/4, I = i/e (as shown in the book)
Substitution;
i/e = i * e^-2(1/4)/L
1/e = e^-2L/4, cancelled out the initial temperatures.
e = e^2L/4, took reciprocal
ln(e) = ln(e^2L/4) = 2L/4ln(e) , log laws
1 = 2L/4
2L = 4
Therefore L = 1/2
ExtremelyBoredUser
Bored Uni Student
This requires previous questions and since you've worked them out, I'll skip the derivations for the sake of time.
Known parameters:
C = 100 * e^lt, B = 525e^kt, C = B, l = ln(217/100)/12, k = ln(122/105)/12.
Now we have to equate them to find when they are equal:
100e^lt = 525e^kt
525/100 = e^lt/e^kt = e^lt * e^-kt = e^lt-kt = e^t(l-k), indice laws
ln(525/100) = t(l-k)
t = ln(21/4)/(l-k)
Substitute the known values for l and k in your calculator. I got 31.854. Round it up and you should get approximately 32 months.
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