Category 5: Exponential Functions

2. A car company is studying the value of its vehicles after they're purchased. A car's value after 𝑥 years of its purchase can be modeled by the function 𝑓(𝑥) = 39850(0.89)ˣ. Which statement is the best interpretation of one of the values in this function?

• 𝑭. The car's value at one year after purchase is approximately $39,850.
• 𝑮. The initial car's value increases at a rate of 89% every year.
• 𝑯. The initial value of the car is $39,850.
• 𝑱. The initial car's value increases at a rate of 11% every year.

4. The concentration of a medicine, measured in milligrams, in a person's body can be given by the exponential function 𝑑(𝑡) = 200(0.8)ᵗ , where 𝑡 is the number of hours since the individual ingested the medication. Which statement is the best interpretation of one of the values in this function?

• 𝑭. The initial concentration of this medicine in a person's body decreases by 20% every hour.
• 𝑮. The initial concentration of this medicine at the time of ingestion was 80 milligrams.
• 𝑯. The concentration of this medicine in a person's body increases at a rate of 80% every hour.
• 𝑱. The concentration of this medicine in a person's body decreases by 20 milligrams every hour.

2. An exponential function is graphed on the grid. Which function is best represented by the graph?

• 
• 
• 
• 

3. The table shows the value in dollars of a luxury vehicle at the end of 𝑥 years. Based on this information, which function best models the value, in dollars, of the vehicle after 𝑥 number of years?

• 
• 
• 
• 

5. Between 1800 and 1900, the total amount of annual carbon emissions in the United States increased at a rate of 6.25%. In 1800, the total carbon emissions in the United States was about 0.25 million tonnes. Which function models the amount of annual carbon emissions in million tonnes after 𝑥 years since 1800?

• 
• 
• 
• 

6. A quantity decreases by 60% every hour. Which of the following is a possible equation for the quantity?

• 
• 
• 
• 

3. The graph of an exponential function is shown on the grid. Which dashed line is an asymptote for the graph?

• 𝑨. Line 𝑎
• 𝑩. Line 𝑏
• 𝑪. Line 𝑐
• 𝑫. Line 𝑑

5. Which graph is best represented by these three descriptions? I. Has an asymptote at 𝑦=0. II. Is decreasing from left to right. III. Has an initial value of 3.

• 
• 
• 
• 

7. Which equation represents the asymptote for the exponential function shown?

• 𝑨. 𝑥 = −2
• 𝑩. 𝑦 = −2
• 𝑪. 𝑥 = −3
• 𝑫. 𝑦 = −3