Interpreting Functions in Terms of Context (Grade 10)

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Interpreting Functions in Terms of Context

1. 
Chloe is trying to save more money for college. She has $5,000 in her account, and will now add $100 each month from her part-time job. The function [math]S(x) = 5","000 + 100x[/math] describes this situation, showing how much money will be in the account after [math]x[/math] months. If Chloe wants to have at least $7,000 in her account, which of the following represents this?
  1. [math]S(x) = 2","000[/math]
  2. [math]x >= 7","000[/math]
  3. [math]S(x) >= 7","000[/math]
  4. [math]x=20[/math]
2. 
The function [math]h(t)[/math] describes the height of a plane, in meters, where [math]t[/math] is the time elapsed since the plane took off, in hours. Which of the following best describes the inequality [math]h(t) < 10","500 ?[/math]
  1. The plane flies for less than 10,500 hours.
  2. The plane can carry less than 10,500 pounds of cargo.
  3. The plane flies below 10,500 meters during its flight.
  4. The total distance the plane flies is less than 10,500 meters.
3. 
If the function [math]P(d)[/math] represents the pressure (in psi) at certain depths (in feet) below the ocean surface, what does the equation [math]P(33) = P(0) + 14.5[/math] mean?
  1. The pressure does not change as one goes deeper in the ocean.
  2. The pressure 33 feet below the surface increases by 14.5 psi.
  3. At a depth of 14.5 feet, the pressure equalizes.
  4. This function can only record pressure for depths of up to 33 feet.
4. 
At a local recycling and garbage facility, people pay for the weight of the trash or recycling they bring in. The function [math]C(w)[/math] gives the cost, [math]C[/math], in dollars that they pay for the weight, [math]w[/math], in pounds that they bring in. What does [math]C(50)=100[/math] mean?
  1. People can only bring in 50 pounds of garbage or recycling.
  2. 100 pounds of garbage or recycling costs 50 dollars.
  3. People can only bring in 100 pounds of garbage or recycling.
  4. 50 pounds of garbage or recycling costs 100 dollars.
5. 
Will is going for a walk on a hiking trail just outside his town. The trail is very hilly. The function [math]h(d)[/math] gives his height, [math]h[/math], in meters above the town according to the distance, [math]d[/math], in kilometers he has walked along the path. What does [math]h(2.5) > h(4)[/math] mean?
  1. The height at 2.5 km along the path is higher than the height at 4 km along the path.
  2. The trial's highest point is at 2.5 km along the path.
  3. The trail is all downhill after 2.5 km along the path.
  4. The height at 4 km along the path is actually below the height of the town.
6. 
A bucket was left outside several days ago, collecting water when it rained and then loosing water when it evaporated. The function [math]W(t)[/math] gives the level of water in inches, depending on t, the number of days since it was first left outside. What does [math]W(2) = W(5)[/math] mean?
  1. The water level was only recorded on the 2nd and 5th days.
  2. The water level was 5 inches on the 2nd day.
  3. The water level was the same on the 2nd day as it was on the 5th day.
  4. The water level was 2 inches on the 5th day.
7. 
The function [math]f(x)[/math] describes the labor costs, [math]f[/math], in dollars at Jim's Hardware for a given month, given the combined number of hours all his employees work, [math]x[/math]. Which of the following would represent the fact that the hardware store's labor costs range between $1,500 and $2,500 each month?
  1. [math]1","500 <= f(x) <= 2","500[/math]
  2. [math]1","500 <= x <= 2","500[/math]
  3. [math] f(x) = 1","000 [/math]
  4. [math]f(1","500) < x < f(2","000)[/math]
8. 
Sally owns a landscaping business. When it comes to mowing lawns, she knows that the time it takes to mow the lawn depends mostly on the size of the lawn. However, for smaller lawns, she has to use a push mower, but for larger lawns, she can use a ride-on lawnmower. If [math]T(s)[/math] represents the function that describes this relationship, where [math]T[/math] is the time is takes to mow a lawn in hours, and [math]s[/math] the size of the lawn in square feet, which of the following represents the fact that mowing a lawn that is 40 square feet takes just as long as mowing a lawn that is 150 square feet?
  1. [math]T(150)=40[/math]
  2. [math]T(40) = T(150)[/math]
  3. [math]T(40) = 150[/math]
  4. This is not a function.
9. 
Lexi had her car towed when it broke down. It cost her $3.50 per mile to have it towed plus a flat fee of $50. The function for her cost was C(m) = 3.50m + 50. If she had it towed 32 miles, how much did it cost her?
  1. $162
  2. $80
  3. $91.50
  4. None of the above
10. 
The function [math]f(x)=50(1.2)^x[/math] gives the number of bacteria in a science experiment, where x is the number days after the start of the experiment. To the nearest whole number, how many bacteria will there be after 5 days?
  1. 124
  2. 375,000,000
  3. 300
  4. 777,600,000

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