MATH01130-5 Mathematica Project Instruction Write your answers in your Mathematica notebook file (*.nb) along with corresponding codes and results, and then send this file to shimh@rowan.edu by Dec 10, 2016. Put Project 1 and 2 into the same file and make sure to indicate your rowan id in the file name. Project 1 (From Exercise 75,76, 4.2) A study shows that the concentration C(t) (in micrograms per milliliter) of antibiotic in a patient's blood serum after t hours is C(t) = 120(e0.2t ebt ), where b 1 is a constant that depends on the particular combination of antibiotic agents used. 1. Solve numerically for the value of b for which maximum concentration occurs at t = 1 h. 2. Find the value of b for which the maximum value of C is equal to 100 mcg/ml. Project 2 (From Exercise 29, 5.9) Moore's Law In 1965 Gordon Moore predicted that the number N of transistors on a microchip would increase exponentially. 1. Does the table of data below confirm Moore's prediction for the period from 1971 to 2000? If so, estimate the growth constant k. 2. Plot the data in the table. 3. Let N (t) be the number of transistors t years after 1971. Find an approximate formula N (t) Cekt , where t is the number of years after 1971. 4. Estimate the doubling time in Moore's Law for the period from 1971 to 2000. 5. How many transistors will a chip contain in 2020 if Moore's Law continues to hold? 6. Can Moore have expected his prediction to hold indefinitely? Processor 4004 8008 8080 8086 286 386 processor 486 DX processor Pentium processor Pentium II processor Pentium III processor Pentium 4 processor Xeon processor Year 1971 1972 1974 1978 1982 1985 1989 1993 1997 1999 2000 2008 No. Transistors 2250 2500 5000 29,000 120,000 275,000 1,180,000 3,100,000 7,500,000 24,000,000 42,000,000 1,900,000,000