Gas Tank Leak Rate Problem: Modeling and Calculating with V(t)=90(1-t/18)^2

In summary, the gas tank of a parked pickup truck develops a leak and the amount of gas remaining can be modeled by the function V(t)= 90(1-t/18)^2. To find the rate of gas leakage at t=12h, the first derivative of V(t) should be computed and evaluated for t=12, resulting in a rate of 3.33 l/h. The book's answer is incorrect.
  • #1
xdeanna
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The gas tank of a parked pickup truck develops a leak. The amount, V, in liters, of gas remaining in the tank after t hours can be modeled by the function
V(t)= 90(1-t/18)^2 , t is between 0 and 18.

b) how fast is the gas leaking from the tank at t=12h

I tried V(12) and V'(12) but still didn't get the answer at the back of the book. Shouldn't it be the first derivative at t=12?
 
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  • #2
xdeanna said:
The gas tank of a parked pickup truck develops a leak. The amount, V, in liters, of gas remaining in the tank after t hours can be modeled by the function
V(t)= 90(1-t/18)^2 , t is between 0 and 18.

b) how fast is the gas leaking from the tank at t=12h

I tried V(12) and V'(12) but still didn't get the answer at the back of the book. Shouldn't it be the first derivative at t=12?

Yes, you should compute
[tex]\frac{dV}{dt}[/tex]
and evaluating for t =12

You should get 3.33 l/h
 
  • #3
Thanks :) I got that too.. the book is wrong
 

FAQ: Gas Tank Leak Rate Problem: Modeling and Calculating with V(t)=90(1-t/18)^2

What is a rate of change problem?

A rate of change problem is a mathematical problem that involves finding the relationship between two quantities that are changing over time. It is used to analyze how one variable affects the other, and to make predictions about future changes.

How do you calculate the rate of change?

The rate of change is calculated by taking the difference between two data points and dividing it by the difference in time between those points. This can be expressed as a ratio or a percentage.

What is the difference between average rate of change and instantaneous rate of change?

The average rate of change is the overall change in a variable over a given period of time, while the instantaneous rate of change is the change at a specific point in time. The average rate of change is calculated by taking the slope of the line connecting two points on a graph, while the instantaneous rate of change is calculated by taking the derivative of a function at a specific point.

How is rate of change used in real life?

Rate of change is used in many real-life applications, such as calculating the speed of a moving object, predicting population growth, and analyzing the effects of interest rates on investments. It is also used in fields such as economics, physics, and engineering to make predictions and inform decision making.

What is the relationship between rate of change and slope?

Rate of change and slope are closely related concepts. The slope of a line is a measure of its steepness and can be calculated by dividing the change in the y-coordinate by the change in the x-coordinate. This is essentially the same as calculating the rate of change between two points on a graph. In other words, the slope of a line is the rate of change of the dependent variable with respect to the independent variable.

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