$5.$ Bummer. Maybe its not the initial stock of resources available to society that matters to the existence of a limit to growth. Lets instead examine a change in the percentage growth rate of population. Going back to the parameter values in question $1$ above $($so r $=2,$ minimum per capita consumption is $50,$ population is $5,000,000$ and the initial stock of resources has its original value of $$150,000,000\mathrm{.}00),$ let$$s cut that assumed growth rate from $20\%$ to $10\%.$

a$.$ does a limit to growth still exist? if so$,$ between what two years is it reached?

b$.$ between what years would society reach a limit to growth if the population growth rate was lowered to $5\%$ instead of $10\%,$ keeping all the other parameters above unchanged

c$.$ will society reach a limit to growth in a finite number of years for any population growth rate greater than $0\%?$