An exponential function f(x) = ab passes through the points (0, 11000) and (3, 5632). What are the values of a and b? a = b= Question Help: Video
An exponential function f(x) = ab passes through the points (0, 11000) and (3, 5632). What are the values of a and b? a = b= Question Help: Video
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.5: Graphical Differentiation
Problem 2E
Related questions
Question
![### Exponential Function Problem
An exponential function \( f(x) = ab^x \) passes through the points (0, 11000) and (3, 5632). What are the values of \( a \) and \( b \)?
#### Given Points:
- (0, 11000)
- (3, 5632)
#### To Find:
- \( a \)
- \( b \)
#### Solution:
Using the given points, set up the following equations based on the exponential function formula \( f(x) = ab^x \).
1. When \( x = 0 \):
\[
11000 = ab^0 \implies 11000 = a(1) \implies a = 11000
\]
2. When \( x = 3 \):
\[
5632 = 11000b^3
\]
3. Solving for \( b \):
\[
\frac{5632}{11000} = b^3 \implies b^3 = \frac{5632}{11000} \implies b = \sqrt[3]{\frac{5632}{11000}}
\]
Plug the values to find the exact numerical value of \( b \).
#### Input Values:
- \( a = \) [Text Box for value]
- \( b = \) [Text Box for value]
#### Additional Help:
For step-by-step solutions and more detailed explanations, please refer to the instructional video linked below:
- [Video Tutorial](#)
Note: Below the problem statement, there are text boxes for inputting the values of \( a \) and \( b \), and a link to a video for further assistance.
---
### Explanation of any Diagrams or Graphs:
The problem does not include any diagrams or graphs; it is purely a textual mathematical problem. The interface shows a small section of a computer screen indicating possible tools like a video help button, presumably for educational purposes.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7167f26-c4aa-4cbc-ab2c-28c429d612af%2Fd256a7e3-4dcb-4e20-85cc-f83879c2811b%2Fyaqpucg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exponential Function Problem
An exponential function \( f(x) = ab^x \) passes through the points (0, 11000) and (3, 5632). What are the values of \( a \) and \( b \)?
#### Given Points:
- (0, 11000)
- (3, 5632)
#### To Find:
- \( a \)
- \( b \)
#### Solution:
Using the given points, set up the following equations based on the exponential function formula \( f(x) = ab^x \).
1. When \( x = 0 \):
\[
11000 = ab^0 \implies 11000 = a(1) \implies a = 11000
\]
2. When \( x = 3 \):
\[
5632 = 11000b^3
\]
3. Solving for \( b \):
\[
\frac{5632}{11000} = b^3 \implies b^3 = \frac{5632}{11000} \implies b = \sqrt[3]{\frac{5632}{11000}}
\]
Plug the values to find the exact numerical value of \( b \).
#### Input Values:
- \( a = \) [Text Box for value]
- \( b = \) [Text Box for value]
#### Additional Help:
For step-by-step solutions and more detailed explanations, please refer to the instructional video linked below:
- [Video Tutorial](#)
Note: Below the problem statement, there are text boxes for inputting the values of \( a \) and \( b \), and a link to a video for further assistance.
---
### Explanation of any Diagrams or Graphs:
The problem does not include any diagrams or graphs; it is purely a textual mathematical problem. The interface shows a small section of a computer screen indicating possible tools like a video help button, presumably for educational purposes.
---
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