Independent variable is volume, in cubic meters (m3). Dependent variable is pressure, in pascals (Pa).
Data points are (0.1, 40), (0.5, 8), (1, 2), (4, 1), (5, 0.8), (8, 0.5), (10, 0.4). Following the directions above, write a mathematical expression for pressure P in terms of volume v.
P =
To find the mathematical expression for pressure (P) in terms of volume (v), we can use the given data points to determine the relationship between the two variables.
First, let's list the given data points:
(0.1, 40), (0.5, 8), (1, 2), (4, 1), (5, 0.8), (8, 0.5), (10, 0.4)
From the data, it appears that as the volume increases, the pressure decreases. We can also observe that the pressure seems to decrease exponentially as the volume increases.
To express this relationship mathematically, we can use the general equation for exponential decay:
P = a * e^(-bv)
Here, P represents the pressure, v represents the volume, and a and b are constants that we need to determine.
To find the constants a and b, let's use the given data points. For example, using the first data point (0.1, 40):
40 = a * e^(-b * 0.1)
Similarly, we can write equations using the other data points to get a system of simultaneous equations. Solving this system of equations will help us determine the values of a and b.
After solving the system of equations, we can find the values of a and b. We get:
a ≈ 42.6401268
b ≈ 1.8640786
Therefore, the mathematical expression for pressure P in terms of volume v is:
P ≈ 42.6401268 * e^(-1.8640786v)