# Lesson 2

Representations of Growth and Decay

- Let’s revisit ways to represent exponential change.

### Problem 1

In 1990, the value of a home is $170,000. Since then, its value has increased 5% per year.

- What is the approximate value of the home in the year 1993?
- Write an equation, in function notation, to represent the value of the home as a function of time in years since 1990, \(t\).
- Will the value of the home be more than $500,000 in 2020 (assuming that the trend continues)? Show your reasoning.

### Problem 2

The graph shows a wolf population which has been growing exponentially.

- What was the population when it was first measured?
- By what factor did the population grow in the first year?
- Write an equation relating the wolf population, \(w\), and the number of years since it was measured, \(t\).

### Problem 3

Here is the graph of an exponential function \(f\).

Find an equation defining \(f\). Explain your reasoning.

### Problem 4

The equation \(f(t) = 24,\!500 \boldcdot (0.88)^t\) represents the value of a car, in dollars, \(t\) years after it was purchased.

- What do the numbers 24,500 and 0.88 mean?
- What does \(f(9)\) represent?
- Sketch a graph that represents the function \(f\) and shows \(f(0), \) \(f(1),\) and \(f(2)\).

### Problem 5

The first two terms of an exponential sequence are 18 and 6. What are the next 3 terms of this sequence?

### Problem 6

A bacteria population has been doubling each day for the last 5 days. It is currently 100,000. What was the bacterial population 5 days ago? Explain how you know.

### Problem 7

Select all expressions that are equivalent to \(27^{\frac13}\).

9

3

\(\sqrt{27}\)

\(\sqrt[3]{27}\)

\(\sqrt[3]{3^3}\)

\(\frac{1}{27}\)

\(\frac{1}{27^3}\)