exam1_solnFall08

# exam1_solnFall08 - Math 116 First Midterm Name Instructor 1...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
page 2 Math 116 / Exam 1 (October 14, 2008) 1 . [10 points] A model 1 for the extinction rate of marine species during the Phanerozoic period (which extends from approximately 545 million years before the present until now) stipulates that this extinction rate, r ( t ), in numbers of marine animal families per million years, is r ( t ) = 3130 t + 262 , where t is the number of million years after the start of the Phanerozoic period. a . [5 points] Find an expression for E ( t ), the number of extinctions that occurred between the start of the Phanerozoic period and t million years thereafter. Solution: Using the fundamental theorem of calculus, this is just E ( t ) = Z t 0 3130 x + 262 dx = (3130 ln | x + 262 | ) ± ± ± t 0 = 3130 ln( t + 262) - 3130 ln(262) . (units are marine animal families). b . [5 points] Find an expression for the average rate of extinctions between the start of the Phanerozoic period and t million years thereafter. Solution: The average rate is A ( t ) = 1 t - 0 Z t 0 3130 x + 262 dx = 1 t (3130 ln( t + 262) - 3130 ln(262)) . (units are marine animal families/million years). 1 Decline in Extinction Rates and Scale Invariance in the Fossil Record , Paleobiology 25 :234–39 (1999)
page 3 Math 116 / Exam 1 (October 14, 2008) 2 . [12 points] Let f ( x ) be a positive, continuous and diferentiable, non-constant Function. Let F ( x ) be an antiderivative oF f that passes through the origin. ±or each oF the Following, ²nd

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/18/2009 for the course MATH 116 taught by Professor Staff during the Fall '08 term at University of Michigan-Dearborn.

### Page1 / 9

exam1_solnFall08 - Math 116 First Midterm Name Instructor 1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online