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

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Chapter1: Functions And Models
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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 \( t = 1000 \).
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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