High School

OPEN UP HS MATH | MATH I

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For problems 6-8, use this situation:

The lake at the Duck Park is contaminated with flesh-eating bacteria! Initially, the lake contained 4 square feet of bacteria. This area is growing by a factor of 3 every hour. Assume that the relationship between hours and square feet of bacteria is continuous.

6. Is this situation linear or exponential? Why?

7. What is the domain for the function that models the relationship between hours and square feet of bacteria?

8. Write an explicit function for the relationship.

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For problems 9-11, use this information:

There is a discrete relationship between the number of workers and the number of bricks laid.

[tex]\[

\frac{3604}{90} = \frac{260}{3} = 90

\][/tex]

9. Is the relationship between workers and bricks laid linear or exponential? Justify your answer.

10. What is the domain for the function that models the relationship between workers and bricks laid on the wall?

11. Write both an explicit and a recursive rule for the relationship between workers and bricks laid.

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Quiz 1: Lessons 1-3

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Answer :

Sure! Let's go through the solution for this question step-by-step.

1. Identify the Type of Relationship:
- Situation Description: The lake initially has 4 square feet of bacteria, and this area increases by a factor of 3 every hour.
- Analysis: Since the bacteria area grows by a constant factor (3) every hour, this is an example of exponential growth. In exponential growth, the quantity increases by a consistent percentage (or factor) over equal increments of time.

2. Determine the Domain of the Function:
- The domain of a function includes all possible values of the independent variable, which in this case is time (t), measured in hours.
- Since time cannot be negative, the domain consists of all non-negative real numbers. Therefore, the domain is [tex]\( t \geq 0 \)[/tex].

3. Write the Explicit Function:
- Initial Area of Bacteria (A\_0): 4 square feet.
- Growth Factor: 3 (area triples every hour).
- The function that models the relationship between time in hours (t) and the area of bacteria (A) is given by:
[tex]\[
A(t) = 4 \times 3^t
\][/tex]
- This function helps calculate the area covered by bacteria after t hours.

In summary, the situation is exponential because the bacteria area grows by a constant factor every hour. The domain of the function is [tex]\( t \geq 0 \)[/tex], and the explicit function modeling this growth is [tex]\( A(t) = 4 \times 3^t \)[/tex].