Scenario: You are a New York City environmental policy analyst tasked with advising the Mayor on how much the city should invest today to prevent $$100$ billion of environmental damage due to climate change in $50$ years.

Tasks:

Skim Future & Present: Where Brains, Math and Ethics Collide and$/$or Hyperbolic discounting $-$ The Decision Lab

Calculate the present value of the damage estimate at r$=7\%$ compounded annually using the standard exponential formula FV$=$PV$\backslash$times $(1+$r$)$t

Cacluate the present value of the damage estimate using k$=15\%$ and the hyperbolic discounting formula: FV$=$PV$\backslash$times $(1+$k$\backslash$times t$)$

What exponential discount rate r would give the same result as the hyperbolic formula?

What is the difference in recommended investments today to prevent the future damage using exponential and hyperbolic discounting?

How much investment do you recommend to the Mayor based on these anlayses? Explain in $2-3$ sentences, using concepts from either or both of the articles linked in $1.$