Download Questions on compound interest and exponential decay

ASSIGNMENT 4
DUE WEDNESDAY, SEP 9
1. RADIOACTIVE CARBON DATING OF ANCIENT ARTIFACTS (BONES, FOSSILS, ETC.,)
Watch video on exponential decay (on Sitaraman’s update page or McGowan’s Blackboard page) if
you are unfamiliar with any of the material on this problem.
All organic matter (plants, animals,…) contain two types of carbon. Carbon-12 which is regular
carbon, and carbon 14 which is radioactive and decays over time. The amount of carbon 14 left in
an organic object can be calculated using the ratio of carbon-12 to carbon-14. The equation for the
amount left A(t) is given by the following equation :
A(t) = A(0) e(-t/8033)
Here A(0) is the original amount, 1/8033 = 0.0001245 is the decay constant. Notice the negative
sign in the exponent. If it were exponential growth, the xponent would be positive.
(a) How much carbon-14 would be left after 1000 years if you start with 100g ?
(b) Find the half-life of carbon-14 (how long would it take for, say, 100g to become 50g? It doesn’t
matter how much you start with, though).
2. CALCULATING AMOUNT OF WINDPOWER THAT CAN BE CREATED
For the following, watch the video lecture by Prof. Schwartzman (titled “Closing words on the
powerpoint by Dr. Schwartzman) if you need additional explanation. In this video Dr. Schwartzman
explains how to calculate the rate at which renewable power (from wind, solar, etc.,) can be built up,
using a feedback mechanism that uses part of the power generated to build more renewable power.
Using the solar calculator at http://solarutopia.org/solar-calculator find out the value of R* (the
ratio of renewables such as wind and solar to the fossil energy such as coal and oil) in 10 years, 20
years and 30 years if L = 25, M = 25, fFF = 0.02 and f = 0.1. Assume some fossil energy is used along
the way. To get this simply plug in the values of M, fFF and f in the boxes provided and look under L
in the table. If R* given by the table represents PRE/PFF where PFF remains fixed (it is the current
power capacity of the world) and PRE is the amount of renewable energy (which grows according to
an exponential equation that you need not worry about),
(a) when do renewables surpass fossil fuels? In other words, if R* = PRE/PFF , then when is R* > 1 ?
(b) If current capacity is 25 trillion watts, then how much will R* be in 25 years?
(c) Now let us compare with what we get using the compound interest formula. If the amount of
renewable power in 2014 was 0.093 trillion watts, and it grows at the rate of 0.16 (or 16%), then
when will there be as much renewable power as the amount you got in part (b) using the solar
calculator website?