klist=1:2:100;

r1=1/5;
r2=1/100;

explist1=exp(-r1*klist);
explist2=exp(-r2*klist);

figure
set(gca,'Fontsize',18)
bar(klist,explist1+explist2)
xlabel('k')
title('sum of exponentials -- well fit my line')

figure
set(gca,'Fontsize',18)
bar(klist,log(explist1+explist2))
xlabel('k')
title('log of sum of exponentials -- not well fit by line')


figure
subplot(121)
set(gca,'Fontsize',18)
bar(klist,(explist1+explist2))
xlabel('k')
title('sum of exponentials, split into two ranges')
axis([0 15 -Inf Inf])
subplot(122)
set(gca,'Fontsize',18)
bar(klist,(explist1+explist2))
xlabel('k')
axis([15 100 -Inf Inf])