Unit 2: Analyzing and Interpreting Exponential Functions

Unit 2: Analyzing and Interpreting Exponential Functions

Multiple Choice

The graph shows an exponential function. What is the equation of the function?

• $$y=\ 3\left(\frac{1}{2}\right)^x$$

• $$y=\frac{1}{2}\left(3\right)^x$$

• $$y=\frac{1}{2}\left(\frac{1}{6}\right)^x$$

• $$y=5\left(2\right)^x$$

Fill in the Blanks

Here is a graph representing an exponential function f. The function f gives the value of a computer, in dollars, as a function of time, x, measured in years since the time of purchase. What is the average rate of change of the value of the computer over the first four years?

Multiple Choice

Use the table to answer the following question. Which equation BEST fits the data in the given table?

• $$y=40\left(2\right)^x$$

• $$y=40\left(\frac{1}{2}\right)^x$$

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and grows by 3% each year. Write an equation that represents this situation.

• y = 5000(0.03)^x

• y = 5000(0.97)^x

• y = 5000(1.03)^x

• y = 5000(3)^x

Multiple Choice

Consider the sequence shown. Which function represents this sequence?

• f(x) = (2)^{x - 1}

• f(x) = (4)^{x - 1}

• f(x) = 2(4)^{x - 1}

• f(x) = 4(2)^{x - 1}

Open Ended

The first five terms of a sequence are shown.

5, 15, 45, 135, 405, ...

What is the common ratio of the function?

Multiple Choice

Suppose a car is worth $22,000 that loses 10% of its value every year. The table shows the value, v, of a car after, t, years.

Write an equation to find the value of the car, v, after t years.

• v(t) = 22,000(0.9)^t

• $$v(t)=22,000(0.9)^{t-1}$$  

• $$v(t)=22,000(1.1)^{t-1}$$  

• $$v(t)=22,000(1.1)^t$$  

Open Ended

Suppose a car is worth $22,000 that loses 10% of its value every year. The table shows the value, v, of a car after, t, years.

Complete the table by finding the missing values.

Fill in the Blanks

Suppose a car is worth $22,000 that loses 10% of its value every year. The table shows the value, v, of a car after, t, years.

What will be the value of the car after 16 years? Answers are rounded to the nearest hundredth.

Multiple Choice

A farmer starts a petting zoo with a family of bunnies. The growth of the bunny population is modeled by $$P\left(x\right)=a_0\ \cdot\ 2^x$$ , where x is the time in weeks and a₀ is the initial amount if bunnies.

According to the given function, what is the rate of growth of the number of bunnies each week?

• 2% growth per week

• 20% growth per week

• 100% growth per week

• 200% growth per week

Multiple Choice

A farmer starts a petting zoo with a family of bunnies. The growth of the bunny population is modeled by $$P\left(x\right)=a_0\ \cdot\ 2^x$$  , where x is the time in weeks and a₀ is the initial amount if bunnies.

If the petting zoo contains 24 bunnies after 3 weeks, how many bunnies did the farmer initially have?

• 3 bunnies

• 12 bunnies

• 384 bunnies

• 768 bunnies

Multiple Select

Which statements are true about the graph of the exponential function f(x)? Select all that apply.

• The y-intercept is 3 and the asymptote is y = -1.

• The x-intercept is 2.

• The domain is all real numbers.

• f(x) is positive for all x-values less than 1.

• As x increases, f(x) approaches, but never reaches, -1.

Open Ended

Estimate the y-intercept.

What does this represent in context?

Open Ended

What are the domain and range of the function?

Open Ended

Why are the x-values nonnegative?