Question

Obtain approximate values of constants c and m for the data at r = 0.1 in...

a) Exponential growth
b) Linear regression
c) Polynomial fit
d) Logarithmic fit

Answer 1

To obtain the approximate values of constants c and m for different types of fits, follow the given steps for each fit type. In exponential growth, use equations 1.1 or 1.2 to calculate M and approximate c and m. In linear regression, find the y-intercept and slope of the line. In polynomial and logarithmic fits, determine the coefficients of the curves.

Step-by-step explanation:

To obtain the approximate values of constants c and m for different types of fits, we can follow the given steps:

a) Exponential growth:

1. Use the equation 1.1 or 1.2 to calculate the value of M at t = 10 or n = 10, respectively.
2. If using equation 1.1, M = M0 * (1 + p)^n, where M0 is the initial size, p is the growth rate, and n is the number of steps. If using equation 1.2, M = M0 * (b^n), where b is the base and n is the number of steps.
3. Approximate the value of c as 1.63 M0, where M0 is the initial size.
4. Approximate the value of m as 0.63, which represents a 63% increase in size.

b) Linear regression:

1. Use a linear regression model to fit the data points and find the equation of the line.
2. The constant c corresponds to the y-intercept of the line, and the constant m corresponds to the slope of the line.

c) Polynomial fit:

1. Use a polynomial regression model to fit the data points and find the equation of the curve.
2. The constant c corresponds to the coefficient of the highest degree term in the polynomial, and the constant m corresponds to the coefficients of the lower degree terms.

d) Logarithmic fit:

1. Use a logarithmic regression model to fit the data points and find the equation of the curve.
2. The constant c corresponds to the vertical shift of the curve, and the constant m corresponds to the scaling factor of the logarithmic function.