Lesson 14

Recalling Percent Change

Let's find the result of changing a number by a percentage.

Problem 1

For each situation, write an expression answering the question. The expression should only use multiplication.

  1. A person's salary is $2,500 per month. She receives a 10% raise. What is her new salary, in dollars per month?
  2. A test had 40 questions. A student answered 85% of the questions correctly. How many questions did the student answer correctly?
  3. A telephone cost $250. The sales tax is 7.5%. What was the cost of the telephone including sales tax?

Problem 2

In June, a family used 3,500 gallons of water. In July, they used 15% more water.

Select all the expressions that represent the number of gallons of water the family used in July.

A:

\(3,\!500 + 0.15 \boldcdot 3,\!500\)

B:

\(3,\!500 + 0.15\)

C:

\(3,\!500 \boldcdot (1 - 0.15)\)

D:

\(3,\!500 \boldcdot (1.15)\)

E:

\(3,\!500 \boldcdot (1+0.15)\)

Problem 3

Han’s summer job paid him $4,500 last summer. This summer, he will get a 25% pay increase from the company.

Write two different expressions that could be used to find his new salary, in dollars.

Problem 4

  1. Military veterans receive a 25% discount on movie tickets that normally cost $16. Explain why \(16 (0.75)\) represents the cost of a ticket using the discount.
  2. A new car costs $15,000 and the sales tax is 8%. Explain why \(15,\!000(1.08)\) represents the cost of the car including tax.

Problem 5

The number of grams of a chemical in a pond is a function of the number of days, \(d\), since the chemical was first introduced. The function, \(f\), is defined by  \(f(d) = 550 \boldcdot \left(\frac{1}{2}\right)^d\).

  1. What is the average rate of change between day 0 and day 7?
  2. Is the average rate of change a good measure for how the amount of the chemical in the pond has changed over the week? Explain your reasoning.
(From Unit 5, Lesson 10.)

Problem 6

A piece of paper is 0.004 inches thick.

  1. Explain why the thickness in inches, \(t\), is a function of the number of times the paper is folded, \(n\).
  2. Using function notation, represent the relationship between \(t\) and \(n\). That is, find a function \(f\) so that \(t = f(n)\).
(From Unit 5, Lesson 8.)

Problem 7

The function \(f\) represents the amount of a medicine, in mg, in a person's body \(t\) hours after taking the medicine. Here is a graph of \(f\).

  1. How many mg of the medicine did the person take?
  2. Write an equation that defines \(f\).
  3. After 7 hours, how many mg of medicine remain in the person's body?
Graph of a decreasing exponential function, origin O. hours after taking medicine and mg of medicine in the body. 

 

(From Unit 5, Lesson 13.)

Problem 8

Match each inequality to the graph of its solution.

A:

\(3x+4y\leq 36\)

B:

\(12x+3y\leq36\)

C:

\(6x+4y\geq36 \)

D:

\(3x-9y\geq 36\)

E:

\(4x-6y\leq 36\)

1:
Inequality graphed on a coordinate plane.
2:
Inequality graphed on coordinate plane, origin O. Scale is negative 10 to 8 on both axes. Line passes through 4 comma 6 and 0 comma 9. The area below the line is shaded.
3:
Inequality graphed on coordinate plane, origin O. Scale is negative 10 to 8 on both axes. Line passes through negative 6 comma negative 6 and 0 comma negative 4. The area below the line is shaded.
4:
Inequality graphed on coordinate plane, origin O. Scale is negative 10 to 8 on both axes. Line passes through 2 comma 6 and 6 comma 0. The area above the line is shaded.
5:
Inequality graphed on coordinate plane, origin O. Scale is negative 10 to 8 on both axes. Line passes through 2 comma 4 and 4 comma negative 4. The area below the line is shaded.
(From Unit 2, Lesson 23.)