# 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:

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

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?