Answer:
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Step-by-step explanation:
In deciding upon the appropriate premium to charge, insurance companies sometimes use the exponential principle, defined as foll
ows. With X as the random amount that it will have to pay in claims, the premium charged by the insurance company is P = 1/a ln(E(e aX )) where a is some specified positive constant. Find P when X is exponential random variable with parameter lambda, and a = alpha lambda, where 0 < alpha < 1.
1 answer:
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Answer:
Step-by-step explanation:
Let x be the number of hours.
We have been given that a vat contains 18 gallons of liquid when a drain pipe opens and the liquid begins to leave the vat at a rate of 4 gallons per hour.
To graph the amount of liquid first of all we will find the equation of line for our given situation.
Since we know that equation of a line in slope-intercept form is: , where, m = slope and b = y-intercept or initial value.
As liquid is leaving the vat at a rate of 4 gallons per hour, this means that amount of liquid in vat in decreasing 4 gallons per hour. As slope is also known as rate of change, so slope of our given line will be -4. A negative slope means that with each increase in x our y will decrease by 4.
As initially there were 18 gallons of liquid in vat, so our y-intercept will be 18.
Upon substituting our given values in slope-intercept form of equation we will get,
Let us find x-intercept by substituting y=0 in our equation.
Now we will draw a line connecting our y-intercept and x-intercept from (0,18) to (4.5,0).
Please find the attachment for the graph of the given line.
