# Lesson 18

Expressed in Different Ways

### Problem 1

For each growth rate, find the associated growth factor.

1. 30% increase
2. 30% decrease
3. 2% increase
4. 2% decrease
5. 0.04% increase
6. 0.04% decrease
7. 100% increase

### Solution

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### Problem 2

In 1990, the population $$p$$ of India was about 870.5 million people. By 1995, there were about 960.9 million people. The equation $$p=870.5\boldcdot \left(1.021\right)^t$$ approximates the number of people, in millions, in terms of the number of years $$t$$ since 1990.

1. By what factor does the number of people grow in one year?
2. If $$d$$ is time in decades, write an equation expressing the number of people, $$p$$, in terms of decades, $$d$$, since 1990.
3. Use the model $$p=870.5\boldcdot\left(1.021\right)^t$$ to predict the number of people in India in 2015.
4. The 2015, the population of India was 1,311 million. How does this compare with the predicted number?

### Solution

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An investor paid $156,000 for a condominium in Texas in 2008. The value of the homes in the neighborhood have been appreciating by about 12% annually. Select all the expressions that could be used to calculate the value of the house, in dollars, after $$t$$ years. A: $$156,\!000\boldcdot\left(0.12\right)^t$$ B: $$156,\!000\boldcdot\left(1.12\right)^t$$ C: $$156,\!000\boldcdot\left(1+0.12\right)^t$$ D: $$156,\!000\boldcdot\left(1-0.12\right)^t$$ E: $$156,\!000 \boldcdot \left(1 + \frac{0.12}{12}\right)^t$$ ### Solution For access, consult one of our IM Certified Partners. ### Problem 4 A credit card has a nominal annual interest rate of 18%, and interest is compounded monthly. The cardholder uses the card to make a$30 purchase.

Which expression represents the balance on the card after 5 years, in dollars, assuming no further charges or payments are made?

A:

$$30(1+18)^5$$

B:

$$30(1+0.18)^5$$

C:

$$30\left(1+\frac{0.18}{12}\right)^5$$

D:

$$30\left(1+\frac{0.18}{12}\right)^{5\boldcdot12}$$

### Solution

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### Solution

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(From Unit 5, Lesson 9.)

### Problem 7

The graph shows the number of patients with an infectious disease over a period of 15 weeks.

1. Give an example of a domain for which the average rate of change is a good measure of how the function changes.
2. Give an example of a domain for which the average rate of change is not a good measure of how the function changes.

### Solution

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(From Unit 5, Lesson 10.)

### Problem 8

A party will have pentagonal tables placed together. The number of people, $$P$$, who can sit at the tables is a function of the number of tables, $$n$$.

1. Explain why the equation $$P = 3n + 2$$ defines this function.
2. How many tables are needed if 47 people come to the party?
3. How many tables are needed if 99 people come to the party?
4. Write the inverse of this function and explain what the inverse function tells us.

### Solution

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(From Unit 4, Lesson 16.)