# GATE Papers >> Civil >> 2017 >> Question No 124

Question No. 124

The infiltration capacity of a soil follows the Horton's exponetial model, $\style{font-family:'Times New Roman'}{f=c_1+c_2e^{-kt}}$. During an experiment the inital infiltration capacity was observed to be 200 mm/h. After a long time the infiltration capacity was reduced to 25 mm/h. If the infiltration capacity after 1 hour was 90 mm/h. the value of the decay rate constant, k (in h-1 up to two decimal places) is ____________.

##### Answer : 0.98 to 1.00

Solution of Question No 124 of GATE 2017 Civil Paper

f = C1 + C2.e-kt

C1 = f0                  C= f1 - f0

= 25 mm/hr       = 200 - 25

= 175

f = 90 mm/hr after 1 hr

Hence, 90 = 25 + 175 x e-kx1

⇒ e-k = $\frac{90-25}{175}$ 0.3715

Taking loge on both side

-k loge e = loge (0.3714)

⇒ -k = -0.990

⇒  k = 0.99

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