Math111i_GroupQuiz5_Solutions

Math111i_GroupQuiz5_Solutions - 0) and their business grows...

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Math 111I Sec 001 Group Quiz 5 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 10 points possible. To receive partial credit on any problem work must be shown. 1. Write a function in the form f ( x ) = C · a x for an exponential function with an initial value of 3,700 whose output triples for each unit increase of the input. Solutions. The initial value is C = 3700, and from the description we see that a = 3. So the function follows as f ( x ) = 3700 · 3 x . 2. Determine if the data is linear or exponential. Write the equation of the function x -1 0 1 2 f ( x ) 3.01 5.50 10.07 18.42 Solutions. We check to see if f ( x ) is exponential 5 . 50 3 . 01 1 . 83 10 . 07 5 . 50 1 . 83 18 . 42 10 . 07 1 . 83 So, we notice that f (0) = C and we have that C = 5 . 50 so we have that f ( x ) = 5 . 50(1 . 83) x . 3. A new cell phone company has 400 subscribes their first year (year
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Unformatted text preview: 0) and their business grows to 600 subscribers the next year (year 1). Write a formula for the number of subscribers, N ( t ), as a function of years in business t , assuming exponential growth. Math 111I Sec 001 Group Quiz 5 Solutions Solutions. Clearly we have that if N ( t ) = Ca t , and we know that N (0) = 400 = C , and we also see that a = 600 400 = 1 . 5 Thus we have that N ( t ) = 400(1 . 5) t . 4. Find the growth/decay factor (assuming exponential growth/decay) for a population that decreases from 11,000,000 to 9,790,000 in one year. Solutions. We have that we decreased over one time period. So the decay factor for each year is a = 11 , 000 , 000 9 , 790 , 000 = 0 . 89...
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Math111i_GroupQuiz5_Solutions - 0) and their business grows...

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