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Common Core Standard HSF-LE.B.5 Questions

Interpret the parameters in a linear or exponential function in terms of a context.

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Grade 9 Functions and Relations CCSS: HSF-LE.B.5
Shawn put some money into an account that earns simple interest according to the function A(t)=1000⋅(1+0.015t), where A is the amount of money in the account after t years. What does the value 1,000 represent?
  1. The total value of money in the account after t years.
  2. The interest earned after t years.
  3. The initial investment.
  4. The interest rate, as a percent.
Grade 9 Functions and Relations CCSS: HSF-LE.B.5
Shea owns a bakery, and primarily sells bread. He has found that he can approximately model his expenses each month with the function E(b)=7b+700, where E is Shea's total monthly expenses in dollars, and b is the number of loaves of bread he sells each month. Which of the following statements about his expenses is correct? There may be more than one correct answer.
  1. His monthly expenses are $707.
  2. It costs about $7 to make each loaf of bread.
  3. Shea has about $700 in fixed expenses each month.
  4. Shea will only break even (make more money than he has to spend in expenses) if he sells at least 100 loaves of bread.
Grade 9 Functions and Relations CCSS: HSF-LE.B.5
Abe is helping to inform people about an upcoming election. He goes door to door, giving out information about the election. He usually visits about 10 houses an hour. He has already been out canvassing for 3 hours, but will stay out longer. Does the function H(t)=30+3t correctly represent the total number of houses Abe will visit, where t is the additional time he will work today? If not, why not?
  1. Yes, this function correctly models this situation.
  2. No, the constant term should be 3, not 30, since he has only been out for 3 hours.
  3. No, the variable H should be measuring how successful he is in convincing people to vote, not simply measuring how many houses he has visited.
  4. No, the coefficient of t should be 10, since he can visit 10 houses per hour.
Grade 9 Functions and Relations CCSS: HSF-LE.B.5
Kyle is an avid bird watcher, and is trying to spot some of the more rare birds in his area. He has already seen 8. However, it has taken 8 months to spot these birds. Kyle's friend is also a bird watcher, and says he typically sees 4 rare birds a month in a large forest outside the town. If Kyle decides to try looking for birds at the forest outside of town, is the linear function B(m)=2+4m correct in predicting the total number of rare birds, B, he will have seen in m months time? If not, why not?
  1. Yes, this function is correct.
  2. No. Kyle has already seen 8 birds, so the constant term should be 8, not 2.
  3. No, since the rate at which Kyle sees birds is incorrect. He has seen 8 birds over 8 months. This means the coefficient of m should be 1, not 4.
  4. No, the equation should be B(m)=4+2m, since 4 represents the number of birds already seen (divided by 2 to account for the 2 sites, the park and the forest), and 2 rare birds per month is the rate at which he will probably see more rare birds.
Grade 9 Functions and Relations CCSS: HSF-LE.B.5
A taxi charges an initial flat fee, plus a per mile rate. If the function T(m)=2.5+0.75m represents the total cost of a trip, where T is measured in dollars and m in miles, what is the per mile rate the taxi charges?
  1. $2.50 per mile
  2. $0.75 per mile
  3. $3.25 per mile
  4. This can't be determined without knowing the exact number of miles the taxi has driven for a specific fare.
Grade 11 Exponents CCSS: HSF-LE.B.5
Carbon dating uses the fact that carbon-14, an element found in nearly all living things, decays exponentially. The function C(t)=5e-0.00012t, models the approximate amount of carbon-14, in micrograms, left in a certain sample of a plant after it died. What does the value 5 represent in this model?
  1. The decay rate constant of carbon-14.
  2. The half life of carbon-14.
  3. The amount of carbon-14 originally in the specimen, in micrograms.
  4. The amount of carbon-14 left in the specimen, in micrograms, after t years.
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