Suppose melting snow causes a river to overflow its banks and h(t) is the number

Question

Suppose melting snow causes a river to overflow its banks and h(t) is the number of inches of water on Main Street t hours after the melting begins. If h'(50) = 1/5, by approximately how much will the water level change during the next half-hour? Which of the following two conditions are the better news? h(50) = 5, h'(50) = 5, h"(50) = - 9 h(50) = 5, h'(50) = -5, h"(50) = 9 In the next half-hour, the water level will change by inches. (Type an integer or a simplified fraction.) The better news would be condition

Explanation / Answer

solution-

a)

there is no information about the relation of h(t) with t so,

assuming the relation is linear.Hence

h(t)=kt

then

h'(t)=k

we have

h'(50)=1/5 which means the slope of line is 1/5 i.e., 1inch per 5 hours

so,

in 1hour level rises 1/8 inch

in 1/2 hour level rises (1/5)*(1/2) = 1/10 inches

hence

water level will change by 1/10 inches .

b)

first condition would be better as-

h'(50)=-5

which means slope is negative means rate of water coming in street is decreasing.

so,

people gets safe from overflow.

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