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- The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?Data were collected from a group of senior citizens, ages 65 and older, about their age and pet ownership. The results were used to calculate the model ŷ = –0.24x + 18.48, where x represents the age in years and ŷ represents the predicted number of pets owned. If a 45-year-old is predicted to have more than 7 pets, would that be a reasonable use of the model? This is not reasonable because the prediction is based on someone outside the original population. This is reasonable because the model is based on real data. This is not reasonable because it is impossible to own more than 7 pets. This is reasonable because the prediction is based on someone within the original population.Data were collected from a group of senior citizens, ages 65 and older, about their age and pet ownership. The results were used to calculate the model ŷ = –0.24x + 18.48, where x represents the age in years and ŷ represents the predicted number of pets owned. If a 25-year-old is predicted to have more than 12 pets, would that be a reasonable use of the model? This is reasonable because the prediction is based on someone within the original population. This is not reasonable because the prediction is based on someone outside the original population. This is reasonable because the model is based on real data. This is not reasonable because it is impossible to own more than 12 pets.
- Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1) where x=0 corresponds to year 1990. A) How many pounds of Aluminum were shipped in 2004 B) Assuming the continued accuracy of the model when will aluminum shipments reach 247,400,000,000 pounds.How do I write the exponential function in the form f(t) = ab^t passing through points (-1, 2/5) and (1, 10)?Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x + 1) where x=0 corresponds to year 1990 a) How many pounds of aluminum were sipped in 2004? b) Assuming the continued accuracy of the model, when will aluminum shipments reach 27,400,000,000 pounds?
- Suppose that poaching reduces the population of an endangered animal by 4% per year. Further suppose that when the population of this animal falls below 70, it's extinction is inevitable. If the current population of the animal is 1500, when will it face extinction?Statistics complied by the local department of corrections indicate that x years from now the number of inmates in-country prisons will be increasing at the rate 280e^0.2x per year. Currently, 2,000 inmates are housed in county prisons. How many inmates should the county expect in 10 years?How do you solve this? The second picture is just the definition of epsilon-neighborhood
- In Exercises 7–12, describe the relationship between the two quantities.Find the work done in emptying the tank in example 4. If the tank water is pumped to a level 1.00 meters above the top of the tank and the water is initially 4.00 meters deep.A culture of bacteria is known to grow at a rate proportional to the present amount. After one hour 100 bacteria are observed in the culture, and 3,000 after four hours. Find the expression for the number of bacteria present in the culture at any time t