Curve fitting with perfect data. Curve fitting allows us to summarize the behavior of a system using a model of the behavior. Later in this course we will fit a curve to the heart rate after exercise to determine the recovery rate. In this example we will consider the growth of bacteria which is modeled as an exponential function A(t)=Pekt where A is the number of bacteria, P is the number of bacteria at time t=0, and k is the constant describing the growth rate. a. Define P=100,k=1, and t as a vector spanning from 0 to 5 hours in 0.1 hour increments. b. Define the time-dependent population of bacteria A according to the equation above. c. Fit a single-term exponential to the data using [cf,gof]=fit(t,A,exp1,startpoint,[1001]); Here 'exp1' specifies a single-term exponential and the name-value pair 'startpoint' specifies the starting guess for P and k. d. Display the goodness of fit information (gof), it should be a perfect fit with R2=1. e. Plot the population data (A) vs time using blue dots ('b.') and the fit (cf) vs time with a red line