The populatoin p of a small community on the outskirts of a city grows rapidly over a 20-year period:
t 0 5 10 15 20
p 100 200 450 950 2000
Fit the data to the model p=C1*exp(C2*t).
a. Apply a transformation to the data and utilize a linear regression to estimate C1 and C2.
b. Create a table, graph and exponential fit in Microsoft Excel. Compare the results.
c. Without transforming the data use fminsearch to estimate C1 and C2.
d. Plot the data and the two fits on the same graph. Be sure to use a legend to identify the fits.