Given that a quantity Q(t) is described by the exponential growth function Q(t) = 308e0.02t where t is measured in minutes, answer the following questions. (a) What is the growth constant k? k = 0.02 (b) What quantity is present initially? 308 units (c) Complete the following table of values. (Round your answers to the near t. 308 10 366 20 448 100 2217 1000 1.46 * 1011
Given that a quantity Q(t) is described by the exponential growth function Q(t) = 308e0.02t where t is measured in minutes, answer the following questions. (a) What is the growth constant k? k = 0.02 (b) What quantity is present initially? 308 units (c) Complete the following table of values. (Round your answers to the near t. 308 10 366 20 448 100 2217 1000 1.46 * 1011
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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WHEN YOU PLUG THE TABLE IN, WHAT IS e???? PLEASE EXPLAIN HOW YOU MULTIPLY OUT THE FORMULA AT THE END
![## Exponential Growth Function
Given that a quantity \( Q(t) \) is described by the exponential growth function:
\[ Q(t) = 308e^{0.02t} \]
where \( t \) is measured in minutes, answer the following questions.
### (a) What is the growth constant \( k \)?
\[ k = 0.02 \]
### (b) What quantity is present initially?
\[ 308 \text{ units} \]
### (c) Complete the following table of values. (Round your answers to the nearest whole number.)
| \( t \) | \( Q \) |
|----------|-----------------------|
| 0 | 308 |
| 10 | 366 (incorrect) |
| 20 | 448 (incorrect) |
| 100 | 2217 (correct) |
| 1000 | \( 1.46 \times 10^{11} \) (correct) |
#### Explanation of the Table:
- The table indicates the values of \( Q(t) \) at different times \( t \).
- The entries for \( t = 10 \) and \( t = 20 \) are marked incorrect, suggesting errors in calculation.
- Correct values are provided at \( t = 100 \) and \( t = 1000 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8719c815-bc4c-45f2-8134-fbe23974a9e7%2F98c955e7-0be9-4b5e-87f6-147ab5f12d31%2Fvav5ok_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Exponential Growth Function
Given that a quantity \( Q(t) \) is described by the exponential growth function:
\[ Q(t) = 308e^{0.02t} \]
where \( t \) is measured in minutes, answer the following questions.
### (a) What is the growth constant \( k \)?
\[ k = 0.02 \]
### (b) What quantity is present initially?
\[ 308 \text{ units} \]
### (c) Complete the following table of values. (Round your answers to the nearest whole number.)
| \( t \) | \( Q \) |
|----------|-----------------------|
| 0 | 308 |
| 10 | 366 (incorrect) |
| 20 | 448 (incorrect) |
| 100 | 2217 (correct) |
| 1000 | \( 1.46 \times 10^{11} \) (correct) |
#### Explanation of the Table:
- The table indicates the values of \( Q(t) \) at different times \( t \).
- The entries for \( t = 10 \) and \( t = 20 \) are marked incorrect, suggesting errors in calculation.
- Correct values are provided at \( t = 100 \) and \( t = 1000 \).
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