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Quiz 6 answer key Math 1030-005 (Fall 2014) 1. You rent time on computers at a local copy center for a $12 setup charge and an additional $3 for every 2 minutes. How much time can you rent for $33? (4 points) Ans: Rate of change: $2/3 for every minute. f (t) = 12 + 2/3t. Set it equal to 33, we have 33 = 12 + 2/3t, where t means “minute”. It solves to t = 31.5 (minutes). 2. The water depth in a lake decreases by 10 inches in 2 days, and 15 inches in 3 days. It seems that the decreased amount is a linear function of t. Find the rate of change: How much does the water depth change per day? (2 points) Use this rate of change to predict how much water depth will decrease in 15 days. (2 points) Ans: 5 inches per day; therefore the predicted decreasing amount is 5 × 15 = 75 (inches). 3. Find an appropriate exponential function to model the following situations: (1) Tom’s house is worth $200000 in 2014, and home prices are rising by 4% every year. What’s the price after t years? (2 points) (2) An antibiotic has half-life in the bloodstream if 12 hours. Assume a 20 mg injection of antibiotic is given at sometime. How much antibiotic remains after t hours? (2 points) Ans: (1) $200000 × (1 + 4%)t . (2) 20 × ( 12 )t/12 (mg).