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Unformatted text preview: Math 111I Sec 001 Test 3 Solutions Name Directions: Read each question carefully and answer in the space pro- vided. The use of calculators is allowed, but not necessary. There are 100 points possible. To receive partial credit on any problem work must be shown. 1. (10 points) An outbreak of a flu virus begins with 5 people infected and the number of people infected increases by a factor of 2.6 each week. (a) Find a formula that gives the number of people infected, I , as a function of the number of weeks, w , since the outbreak. (b) Use this formula to find the number of people infected after 10 weeks. Solutions. (a) Because the spread of flu is a factor of 2.6 people per week that means that the number of infected grows by a multiple of 2.6 people per week. So we see that the growth factor is 2.6 people per week. So with an initial amount of 5 people we see that the equation for the number of people effected is I ( w ) = 5(2 . 6) w . (b) We want to know the number of people infected after 10 weeks. So we want to know I (10). That is I (10) = 5(2 . 6) 10 = 70583 . 5 2. (5 points) Write the function f ( x ) where f (0) = 490, and for every unit increase in x , then output is multiplied by 1.3. Solutions. This is based on the definitions of exponential functions the answer is f ( x ) = 490(1 . 3) x 3. (15 points) Find the equation for the given functions f ( x ) and g ( x ). x f ( x )-1 5.50 7.30 1 9.10 2 10.90 x g ( x )-1 3.01 5.50 1 10.07 2 18.42 Math 111I Sec 001 Test 3 Solutions Solutions. For f ( x ) we begin by noticing that 5 .....
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- Fall '08