Exam 2: Nonlinear Functions and Models

The fuel efficiency (in miles per gallon)of a sport utility vehicle (SUV)depends on its weight according to the formula where x is the weight of an SUV in pounds. According to the model, what is the weight of the least fuel-efficient SUV?

How long will it take an investment to triple if it is continuously compounded at 15% per year? Select the correct answer rounded to the nearest year.

The table lists interest rates on long-term investments (based on 10-year government bonds)in several countries in 2004-2005. Assuming that you invest $13,000 in Japan, how long (to the nearest year)must you wait before your investment is worth $19,000 if the interest is compounded annually? Country U.S. Japan Canada Yield 5.3% 1.5% 5.2% __________ year(s)

The amount of carbon-14 remaining in a sample that weighs A is given by where t is time in years. If tests on a fossilized skull reveal that 99.97% of the carbon-14 has decayed, how old is the skull? Select the correct answer rounded to the nearest integer.

Given the graph of the functions and . Determine the color of the graph that corresponds to . Select the correct answer.

The graph shows the actual percentage of U.S. households with a computer as a function of household income (the data points)and a logistic model of these data (the curve). The logistic model is where is the household income in thousands of dollars. According to the model, what percentage of extremely wealthy households had computers? P = __________%

Soon after taking an aspirin, a patient has absorbed 350 mg of the drug. If the amount of aspirin in the bloodstream decays exponentially, with half being removed every 2 hours, find the time it will take for the amount of aspirin in the bloodstream to decrease to 290 mg. Select the answer rounded to three decimal places.

Plutonium-239 is used as a fuel for some nuclear reactors and also as the fissionable material in atomic bombs. It has a half-life of 24,400 years. How long will it take 14 grams of plutonium-239 to decay to 1 grams? Select the correct answer rounded to the nearest integer.

Find the associated exponential decay model. when ; Half-life =

Find the vertex of the graph of the quadratic function.

Choose the logistic function that best approximates the curve.

Choose the logistic function that best approximates the curve.

Find the logistic function with the given properties. , has limiting value , and for small values of , is approximately exponential and doubles with every increase of 1 in .

For the following demand equation, express the total revenue R as a function of the price p per item.

Model the data using an exponential function .

For the following demand equation, find the largest possible revenue. $ __________

Which of the following three functions will be smallest for large values of x ? Select the correct answer.

The following graph shows the actual percentage of U.S. households with a computer as a function of household income (the data points)and a logistic model of these data (the curve). The logistic model is where is the household income in thousands of dollars. For low incomes, the logistic model is approximately exponential. Which exponential model best approximates for small ? Round the coefficients to the nearest hundredth.

Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if the company builds 60 houses in this particular development, it can sell them for $180,000 each, but if it builds 70 houses, it will be able to get only $170,000 each. What is the largest possible revenue the company can get?

Model the data using an exponential function . Select the correct answer.