# 227 Sales Decline

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Topic : Sales decline Question : How many will they have in stock?A t-shirt company noticed that sales of blue shirts had declined exponentially at a rate of 23%  per year. They currently have 300  blue shirts in stock and they don’t plan to purchase any more. How many blue shirts will they have in stock in 3  years? Answer choices :A 250 B 200 C 150 D 100 176  Solution : CWe can use the exponential decay equation S  ( t  ) =  S  0 e −  λ t  where S  ( t  )  is the final amount after time t  , S  0  is the initial amount, and  λ  is the rate of decline.Remember to make sure that rate of decline and time are in the same units (if your rate of decline is annual, time should be in years). S  ( t  ) = 300 e − 0.23(3) S  ( t  ) = 150 The t-shirt store will have 150  blue t-shirts left in 3  years. 177  Topic : Sales decline Question : How long will it take to increase the stock?The pet store noticed that sales of generic cat food was declining at an exponential rate of 8%  per year. They currently have 600  bags of generic cat food in stock. Assuming that they do not add any more bags to their inventory, how many years will it take for their stock level to get to 100  bags? Answer choices :A 22.4  yearsB 24.4  yearsC 24.2  yearsD 42.4  years 178  Solution : AWe can use the exponential decay equation S  ( t  ) =  S  0 e −  λ t  where S  ( t  )  is the final amount after time t  , S  0  is the initial amount, and  λ  is the rate of decline.Remember to make sure that rate of decline and time are in the same units (if your rate of decline is annual, time should be in years). 100 = 600 e ( − 0.08) t  100600=  e ( − 0.08) t  16=  e ( − 0.08) t  ln16= ln ( e ( − 0.08) t  ) ln16= ( − 0.08) t t   =ln  16 − 0.08 t   = 22.4 It will take the pet store 22.4  years to reduce their stock of generic cat food to 100  bags. 179

Sep 10, 2019

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Sep 10, 2019
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