clc %clear console and return cursor to home
format long

%actual function
tm = linspace(0,10,100);
N0 = 10;
R0 = 0.75;
Nd_smth = N0*exp(R0*tm); 
M = length(Nd_smth);

%generate vals from random distr with mean = mn and stdv = stdv
rng('default'); %fix seed for random # generator to matlab startup seed
mn = 0; %mean
stdv = 1000;
r_pb = mn + stdv.*randn(1,M); 
Nd = r_pb+Nd_smth; %data
plot(tm,Nd,'bx')
N = @(N0,R0,t) N0.*exp(R0*t); %function handle to your exponential fctn

%part 1
% use your solution from 34.14 part c) to solve for N0 and R0 an plot it
%
%N0 = ? 
%R0 = ?
%
%plot(t,Nd,'bx',t,N(N0,R0,t),'r-')




%part 2
% Use gradient descent to find N0 and R0 directly from the original problem
% formulatiom in 34.14 part a)