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Appc 2.3 Ca1

The document provides exercises on identifying exponential functions as growth or decay, along with justifications. It includes tasks to write functions based on given output values and answer questions about their behavior, such as increasing/decreasing and concavity. Additionally, it presents limits for various functions to be calculated.

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32 views2 pages

Appc 2.3 Ca1

The document provides exercises on identifying exponential functions as growth or decay, along with justifications. It includes tasks to write functions based on given output values and answer questions about their behavior, such as increasing/decreasing and concavity. Additionally, it presents limits for various functions to be calculated.

Uploaded by

eyps4e
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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2.

3 Exponential Functions
AP Precalculus Name: _____________________________ CA #1
Identify if the function is exponential growth or decay and justify your response.
1. 𝑓 𝑥 2.5 2. 𝑓 𝑥 3. 𝑓 𝑥 5.7 0.2 4. 𝑓 𝑥 8 2.1

Exponential Exponential
Exponential Exponential Growth or Decay Growth or Decay
Growth or Decay Growth or Decay

The following values are output values of an exponential function of the form 𝒇 𝒙 𝒂 ∙ 𝒃𝒙 ,
where 𝒂 and 𝒃 are constants. Write the function along with the input value that represents the
output value.
5. 7 ⋅ 7 ⋅ 7 ⋅ 3.4 6. 0.8 ⋅ 0.8 ⋅ 5.2 7. 6 ⋅ 1.3 ⋅ 1.3 ⋅ 1.3 ⋅ 1.3 8. 9 ⋅ 9 ⋅ 9

𝑓 𝑥 𝑓 𝑥 𝑓 𝑥 𝑓 𝑥

where 𝑥 where 𝑥 where 𝑥 where 𝑥

Answer the questions for each exponential function.


9. 𝑓 𝑥 10. 𝑓 𝑥 3 4.5

a. Is the function increasing or decreasing?


a. Is the function increasing or decreasing?

b. Is the function concave up or concave down?


b. Is the function concave up or concave down?

c. Find lim 𝑓 𝑥
c. Find lim 𝑓 𝑥 →
→
d. Find lim 𝑓 𝑥
d. Find lim 𝑓 𝑥 →
→

11. 𝑓 𝑥 5 0.8 12. 𝑓 𝑥 2 6

a. Is the function increasing or decreasing? a. Is the function increasing or decreasing?

b. Is the function concave up or concave down? b. Is the function concave up or concave down?

c. Find lim 𝑓 𝑥 c. Find lim 𝑓 𝑥


→ →

d. Find lim 𝑓 𝑥 d. Find lim 𝑓 𝑥


→ →

© The Algebros from FlippedMath.com


Answers to 2.3 CA #1
1. Decay because 𝑎 0 and 2. Decay because 𝑎 0 and 3. Decay because 𝑎 0 and 4. Growth because 𝑎 0
0 𝑏 1 0 𝑏 1 0 𝑏 1 and 𝑏 1

5. 𝑓 𝑥 3.4 7 where 𝑥 3 6. 𝑓 𝑥 5.2 0.8 where 𝑥 2 7. 𝑓 𝑥 6 1.3 where 𝑥 4


9. 10. 11. 12.
a. Decreasing a. Increasing a. Increasing a. Decreasing
b. Concave up b. Concave up b. Concave down b. Concave down
8. 𝑓 𝑥 9 where 𝑥 3 c. lim 𝑓 𝑥 ∞ c. lim 𝑓 𝑥 0 c. lim 𝑓 𝑥 ∞ c. lim 𝑓 𝑥 0
→ → → →
d. lim 𝑓 𝑥 0 d. lim 𝑓 𝑥 ∞ d. lim 𝑓 𝑥 0 d. lim 𝑓 𝑥 ∞
→ → → →

© The Algebros from FlippedMath.com

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