Concept explainers
Extinction The probability of a population going extinct by time
Where
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Calculus For The Life Sciences
- Population The population P (in millions) of Italy from 2003 through 2015 can be approximated by the model P=57.59e0.0051t, where t represents the year, with t=3 corresponding to 2003. (a) According to the model, is the population of Italy increasing or decreasing? Explain. (b) Find the populations of Italy in 2003 and 2015. (c) Use the model to predict the populations of Italy in 2020 and 2025.arrow_forwardPopulation The population P (in millions) of Italy from 2003 through 2015 can be approximated by the model P=57.59e0.0051t, where t represents the year, with t=3 corresponding to 2003. (Source: U.S. Census Bureau) (a) According to the model, is the population of Italy increasing or decreasing? Explain. (b) Find the populations of Italy in 2003 and 2015. (c) Use the model to predict the populations of Italy in 2020 and 2025.arrow_forwardRunning Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runners time at the end of each lap, obtaining the data in the following table. aWhat was the mans average speed rate between 68 s and 152 s? bWhat was the mans average speed between 263 s and 412 s? cCalculate the mans speed for each lap. Is he slowing down, speeding up or neither? Time s Distance m 32 200 68 400 108 600 152 800 203 1000 263 1200 335 1400 412 1600arrow_forward
- Running Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner’s time at the each of each lap, obtaining the data in the following table. (a) What was the man’s average speed (rate) between 68 s and 152 s? (b) What was the man’s average speed between 263 s and 412 s? (c) Calculate the man’s speed for cadi lap, Is he slowing down, speeding up, or neither?arrow_forwardStock Turnover at Retail In retail sales, an important marker of retail activity is the stock turnover at retail. This figure is calculated for a specific period of time as the total net sales divided by the retail value of the average stock during that time, where both are measured in dollars. As a formula, this is written Stockturnover=NetsalesAveragestockatretail. This formula expresses stock turnover as a function of net sales and average stock at retail. a. Suppose that your store had net sales of 682, 000 in mens shoes over the past six months and that the retail value of the average stock of mens shoes was 163, 000. What was the stock turnover at retail for that time period? b. Suppose that in a certain month, your stores net sales of womens dresses were 83, 000 and that the usual stock turnover at retail is 0.8 per month. What do you estimate to be your stores average stock at retail? c. Solve the equation for average stock at retail- that is, write a formula giving average stock at retail as a function of stock turnover and net sales. d. Suppose that in a certain time period, your store had an average stock of socks with a retail value of 45, 000 and a stock turnover at retail of 1.6. What were the stores net sales of socks during that time period? e. Solve the equation for net sales- that is, write a formula giving net sales as a function of stock turnover and average stock at retail.arrow_forward
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