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grigory [225]
4 years ago
7

Determine the growth factor corresponding to 1% increase

Mathematics
2 answers:
bezimeni [28]4 years ago
4 0
Not sure but I would say 0.1 again I am not sure that that is what is asking for
Juliette [100K]4 years ago
3 0

For an increase of percentage, it is a growth factor.

For a decrease of percentage, it is a decay factor.

The growth factor is = (1+r)

The decay factor is= (1-r)

As it is increase of 1%, it is a growth factor.

Here the rate of increase is 1% = 1/100 = 0.01

Hence the growth factor is 1 + 0.01 = 1.01

The growth factor corresponding to 1% increase is 1.01.

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Artyom0805 [142]
A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.
\frac{dT}{dt} = \alpha(T -52)

B) Find general solution by separating variables and integrating\int\frac{dT}{T-52} = \alpha \int dt   \\  ln (T-52) = \alpha t + C  \\  T = C e^{\alpha t} +52:


C) Initial condition is t=0, T = 87
87 = C +52 \\  C = 35

D) Total time elapsed is 10 minutes, new temperature is 84
84 = 35 e^{10\alpha} +52
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e^{10\alpha} =\frac{32}{35}  \\  \alpha = \frac{ln(32/35)}{10} \\  \alpha = -.00896

E) Temperature function is:
T = 35 e^{-.00896 t} +52
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t = \frac{ln (\frac{T-52}{35})}{-.00896}
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