Answer:
-$7.905 per day
Step-by-step explanation:
In this question, given that a tank is losing its fuel content at a certain rate, we are to calculate the rate at which the value in dollars of the content of the fuel tank
is changing
Please check attachment for complete solution and step by step explanation
An underground gasoline storage tank is leaking. The tank currently contains 600 gallons of gasoline and is losing 3.1 gallons per day. The rate at which the value of the stored gasoline is changing is -$7.905 per day.
Suppose we make an assumption that the tank initial contains h(x) gallons of gasoline which leak in x days. Then, the rate of change of gasoline per gallon is;
[tex]\mathbf{\dfrac{dh}{dx} =- 3.1 \ \ \ \ \ \ \text{since the gas is leaking (-)}}[/tex]
Also, the rate of change of the gasoline in time(t) per unit change in the quantity can be computed as:
[tex]\mathbf{\dfrac{dt}{dh}=2.55 }[/tex]
Therefore, the value of the stored gasoline changing per unit change of days can be deduced by using the chain rule:
[tex]\mathbf{\dfrac{dt}{dx} = \dfrac{dt}{dh} \times \dfrac{dh}{dx}}[/tex]
[tex]\mathbf{\dfrac{dt}{dx} = -3.1 \times2.55}[/tex]
[tex]\mathbf{\dfrac{dt}{dx} =\$-7.905 \ per \ day}[/tex]
Therefore, we can conclude that the rate at which the value of the stored gasoline is changing is -$7.905 per day.
Learn more about chain rule here:
https://brainly.com/question/23729337?referrer=searchResults
