Sample Midterm 2 WI 06

# Year number of reported cases 1970 21168 1980 10584

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Year Number of Reported Cases 1970 21,168 1980 10,584 1990 5,292 Assume that N is the number of reported cases t years after 1970. Which of the following would be a good model for N ( t )? i. 21 , 168 (2) t ii. 21 , 168 1 2 t iii. 21 , 168 1 2 t/ 10 iv. 21 , 168 (2) t/ 10

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Form A Page 7 of 7 7. The population of fruit flies in a certain research experiment grows exponentially. Researchers use the formula f ( t ) = Pe rt to model the population after t days. Measurements indicate that f (0) = 30 and f (5) = 1620 . ( All answers must be accurate to 3 decimal places .) (a) Find a function of the form f ( t ) = Pe rt that models the fruit fly population after t days. (7 points) (b) When the function f is expressed in the form f ( x ) = Pa x , the constant a is called the growth factor. Find the growth factor for the function f. (3 points) (c) When will there be 18 , 000 fruit flies? (You may use either form f ( t ) = Pe rt or f ( x ) = Pa x ) (6 points)
Some useful formulas: log ( uw ) = log ( u ) + log ( w ) log ( u c ) = c log ( u ) A = P (1 + r ) t A = P · e rt A = P 1 + r n nt f ( x ) = P · a x d = ( x 1 - x 2 ) 2 + ( y 1 - y 2 ) 2 Area s = θ 360 ( π · r 2 ) cos 2 θ + sin 2 θ = 1 a sin A = b sin B = c sin C a 2 = b 2 + c 2 - 2 bc cos A
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