1. The following graph shows the number, in millions, of students graduating from high school in the U.S., in the given year.
In 1985 2.83 million students graduated. In 1987 2.65 million graduated In 1989 2.47 millionn graduated In 1991 2.29 million graduated t=Year and N=Number graduatiing
a. Explain in practical terms what N(1989) means and find its value.
b. Use functional notation to express the number of graduates in 1988 and estimate its value.
c. Find the average rate of change per year during the period 1989 1991.
d. Use part c to try to estimate N(1992)
0. The following graph shows a population N=N(d), where d is the date.
a. Is the function increasing, decreasing, or neither for d from 2006 to 2016?
b. When is the function concave down and when is it concave up? Give the ranges in years.
c. At what date is there an inflection point?
0. You currently have $780 in your bank account, which pays no interest. You withdraw $39 each week. Find a formula for the balance B, in dollars, in the account after t weeks.
0. One cell phone plan charges a flat monthly rate of $39.95 with extra charges of $0.10 per text message after the first 100 text messages.
a. Choose letters to represent the variables
b. Write a formula to express the cell phone charges as a function of the number of text messages (assume that the number of text messages is at least 100.)
c. Use functional notation to represent the cost of the cell phone if you have 450 text messages.
d. Use the formula from part b to calculate the cost.
e. Write a formula to express the charges assuming the number of text messages is less than 100.
0. It starts to snow when there is already snow on the ground. The depth, in inches, of the snow t hours later is given by S(t)=10.00 + 0.4t.
?
a. How much snow was on the ground when the snow started to fall?
b. By how much did the depth of snow increase from hour 3.00 to hour 6.00?
c. Snow ceases to fall after 10 hours. What is the resulting depth of snow on the ground?
0. The following table shows the U.S. population, in millions, in the given year.
d = year
1960
1970
1980
1990
2000
N= population in millions
179.32
203.3
226.54
248.71
281.42
?
a. Calculate the average rate of change from 1980 to 1990
b. Use the average rate of change to estimate the U.S. population in 1982.
0. A hot potato is placed on the kitchen counter to cool. Its temperature after t minutes is given by T(t). The temperature of the kitchen is 74 degrees Fahrenheit. What is the limiting value of ?T?
0. The graph below shows the growth rate G, in water fleas per day, of a population of water fleas as a function of the population size N. Calculate the average rate of change in G from 130 to 160 water fleas. Round to 3 decimal places.
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0. You sell earrings for $6.33 each. You paid $57.21 for supplies to make the earrings. Write a formula for the profit P, in dollars, you make from making and selling E earrings, where the most earrings you can make with the supplies is 26.
0. The weight W, in pounds, of a rock is proportional to its volume V, in cubic inches. The constant of proportionality is the density, d, in pounds per cubic inch.
?
a. Write a formula that expresses the proportionality relationship.
b. What is the weight of a rock that has a density of 1.02 pounds per cubic inch and a volume of 14 cubic inches?
0. The world record time for a certain track event in 2000 was 74.98 seconds. In the ensuing years, the record time has decreased by 0.94 seconds each year.
?
a. Write a formula for the record R, in seconds, t years after 2000.
b. Use functional notation to express the record in 2002.
c. Calculate the value you found in part B
0. You start with $32.28 in your piggy bank and add $9.28 each week. Write a formula for the amount P of money, in dollars, in your piggy bank after t weeks.
0. The graph below shows the value, in dollars, of a foreign currency t years after 2000.
In what year from 2000 to 2020 did the value of the foreign currency reach its maximum, and what was that maximum value?
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