Graphs of Exponential Functions

​March 14, 2023

​Agenda:

1. Log in to Quizizz.

2. Short Discussion: Graphs of Exponential Function

3. Review for Post Assessment

Fill in the Blank

What is the 10th term of the geometric sequence 3, 6, 12, 24, 48, ...? (no spaces)

Multiple Choice

What equation can represent the given function?

• $$y=8\left(\frac{1}{2}\right)^x$$

• $$y=8\left(2\right)^x$$

• $$y=2\left(\frac{1}{2}\right)^x$$

• $$y=8\left(1.5\right)^x$$

Multiple Choice

John opens his saving account with an initial amount of $100, if it has an annual rate of 4%, what function could represent John's savings in x years?

• $$y=100\left(1.4\right)^x$$

• $$y=100\left(1.04\right)^x$$

• $$y=100\left(0.96\right)^x$$

• $$y=100\left(1.04\right)^{\left(x-1\right)}$$

Graph of an Exponential Function

​is the value in which the graph approaches to but don't intersect.

Horizontal Asymptote

Multiple Choice

What is the horizontal asymptote of the given graph?

• y = 0

• y = 1

• y = -1

• y = 2

Multiple Choice

What is the horizontal asymptote of the given graph?

• y = -2

• y=2

• y=0

• y=1

​Review for

Post-Assessment

Multiple Choice

Which of the following does not represent an exponential growth?

• $$y=\frac{1}{2}\left(1.02\right)^x$$

• $$y=3\left(0.67\right)^x$$

• $$y=8\left(1.03\right)^x$$

• $$y=\left(1.003\right)^x$$

Fill in the Blank

If $$f\left(x\right)\ =\ 4\left(3\right)^x$$ , what is f(5)?

Multiple Choice

What is the domain of the given graph?

• All real numbers.

• $$x\ge0$$

• $$x\le0$$

• All integers.

Multiple Choice

Which exponential function matches with the graph?

• $$y=\ 27\left(\frac{1}{3}\right)^x$$

• $$y=27\left(3\right)^x$$

• $$y=9\left(\frac{1}{3}\right)^x$$

• $$y=3\left(\frac{1}{3}\right)^x$$

Multiple Choice

The population of a town is 12,000, and it grows at a rate of 5% per year. What exponential function could represent this situation?

• $$y=12000\left(1.05\right)^x$$

• $$y=12000\left(1.5\right)^x$$

• $$y=12000\left(0.95\right)^x$$

• $$y=12000\left(1.005\right)^x$$

Multiple Choice

The population of a town is 12,000, and it grows at a rate of 5% per year. What is the population after 4 years?

• about 14500 people

• about 14602 people

• about 14586 people

• about 14592 people

Multiple Choice

The population of a town is in t years after the year 2001 can be modeled by the function $$P\left(t\right)=20000\left(0.91\right)^x$$ , which of the following statements is true?

• The population is increasing at a rate of 9% per year.

• The population is decreasing at a rate of 91% per year.

• The population is decreasing at a rate of 9% per year.

• The population is increasing at a rate of 91% per year.

Multiple Choice

A culture of bacteria doubles every 3 hours. If there are 200 bacteria present at the beginning, if the pattern goes on, which function best describes the number of bacteria in n hours?

• $$y=200\left(\frac{1}{3}\right)^{\left(n-1\right)}$$

• $$y=200\left(3\right)^{\left(n-1\right)}$$

• $$y=200\left(\frac{1}{3}\right)^n$$

• $$y=3n+200$$

Multiple Choice

Simplify: $$\sqrt[3]{64x^{12}y^{21}}$$

• $$3x^4y^7$$

• $$2x^4y^7$$

• $$4x^4y^7$$

• $$12x^4y^7$$

Multiple Choice

An exponential function g(x) is graphed, and another exponential function is represented by $$f\left(x\right)\ =\ 27\left(\frac{1}{3}\right)^x$$ . Which function is greater when x = 2?

• g(x); 4

• f(x); 3

• g(x) = 5

• f(x); 4

Multiple Choice

Given the sequence, 100, 50, 25, 12.5, ..., what is explicit formula and the 10th term of the sequence?

• $$a_n=100\left(\frac{1}{2}\right)^{\left(n-1\right)};\ 0.195$$

• $$a_n=100\left(2\right)^{\left(n-1\right)};\ 51\ 200$$

• $$a_n=100\ \left(2\right)^n;\ 52,\ 100$$

• $$a_n=100\left(\frac{1}{2}\right)^n;\ 0.195$$