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- The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 500 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled by A(n) = (500 + n)(10 − 0.01n) where n is the number of additional vines planted. Find the number of vines that should be planted to maximize grape production.At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 700 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled by A(n) = (700 + n)(10 − 0.01n) where n is the number of additional vines planted. Find the number of vines that should be planted to maximize grape production.
- During a recession, Congress decides to stimulate the economy by providing funds to hire unemployed workers for government projects. Suppose that t months after the stimulus program begins, there are N(t) thousand people unemployed, where N(t)=−t^3+39t^2+406t+3088 To avoid overstimulating the economy (and inducing inflation), a decision is made to terminate the stimulus program as soon as the rate of unemployment begins to decline. When does this occur and at this time, how many people are unemployed?At a certain vineyard it is found that each grape vine produces about 10 lbs of grapes in a season when about 500 vines are planted per acre. for each additional vine that is planted, the production of each vine decreases by 1 percent. So the number of pounds of grapes produced per acre is modeled by: A(n)= (500+n)(10-0.01n) where n is the number of additional vines planted. Find the number of vines that shold be planted to maximize grape production.Between 2005 and 2009, the percentage of people who own a home has changed drastically from state to state. The percentage of individuals who own a home in Indiana can be modeled by C(t) = –0.6t + 76, where t is the number of years since 2005. For New Hampshire, the same model isgiven by N(t) = 0.5t + 73. Did or will Indiana and New Hampshire ever have the same homeownership rate?
- How does h(n) = n2 / 2n behave for large whole-number values of n? Does h(n) tend to infinity?How did you apply the concept of maxima/minima in answering the problem? Angelo, who is in a rowboat 2 kilometers from a straight shoreline wishes to go back to his house, which is on the shoreline and 6 kilometers from the point on the shoreline nearest Angelo. If he can row at 6 kph and run at 10 kph, how should he proceed to get to his house in the least amount of time?. A woman saved GH¢ 30,000 in a bank A, whose rate was x % per annum and GH¢ 20,000 in another bank B whose interest rate was y % per annum. Her total interest in two years was GH¢ 6,400. If she had saved GH¢ 20,000 in bank A and GH¢ 30,000 in bank B for the same period, he would have gained GH¢ 200 as additional interest. Find the values of X and Y
- A house is purchased for $140,000 in January 2004. A year later, the house next door is sold for $149,800. The two houses are of the same style and size and are in similar condition, so they should have equal value.Use the model v = 140e0.0676586485t, where t is the number of years after January 2004 and v is the value in thousands of dollars, to predict when the house would be worth $290,000.Wksp 5 Q8 Give a counterexample to the converse of the problem attachedA certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t)=(493)4 ^1/2, where t represents the number of years from the time of introduction. How long will it take for the population to reach 7888 deer, according to this model?
