Use the table to answer the question.

Question

x 320
0
1
2
3
4
5


Cason is scheduled to get his wisdom teeth removed. The oral surgeon gives him a local anesthetic to numb his mouth before surgery. Cason is given 320 milligrams of the anesthetic, which metabolizes at a rate of 25% per hour. The situation can be modeled using the exponential equation f(x)=320(0.75)x
. Finish the chart to determine which graph displays the correct plotted points for the situation.

Option #1:

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for hours ranges from 0 to 7 in increments of 1. The y-axis for milligrams ranges from 0 to 350 in increments of 50.



Option #2:

A curve with an arrow on the top is plotted on a coordinate plane. The x-axis for hours ranges from 0 to 350 in increments of 50. The y-axis for milligrams ranges from 0 to 7 in increments of 1.



Option #3:

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for hours ranges from 0 to 7 in increments of 1. The y-axis for milligrams ranges from 0 to 350 in increments of 50.

(1 point)
The graph with the correct plotted points is Option #

Answer 1

To determine which graph displays the correct plotted points for the situation, we can calculate the values of \( f(x) \) using the formula \( f(x) = 320(0.75)^x \) for \( x = 0, 1, 2, 3, 4, 5 \).

1. For \( x = 0 \): \[ f(0) = 320(0.75)^0 = 320(1) = 320 \]

2. For \( x = 1 \): \[ f(1) = 320(0.75)^1 = 320(0.75) = 240 \]

3. For \( x = 2 \): \[ f(2) = 320(0.75)^2 = 320(0.5625) = 180 \]

4. For \( x = 3 \): \[ f(3) = 320(0.75)^3 = 320(0.421875) \approx 135 \]

5. For \( x = 4 \): \[ f(4) = 320(0.75)^4 = 320(0.31640625) \approx 101 \]

6. For \( x = 5 \): \[ f(5) = 320(0.75)^5 = 320(0.2373046875) \approx 76 \]

Now, we compile the points:

• \( (0, 320) \)
• \( (1, 240) \)
• \( (2, 180) \)
• \( (3, 135) \)
• \( (4, 101) \)
• \( (5, 76) \)

From the provided options, options 1 and 3 are the only ones that mention a decreasing curve which aligns with our calculations showing that the values are decreasing.

Since both options 1 and 3 look similar, we will determine if they are identical. Given that they both plot the milligrams on the y-axis and hours on the x-axis, we can conclude:

Option #1 and Option #3 correctly represent a decreasing curve for the function, but since they both also align with the stated configuration of axes, you can reasonably choose either.

Thus, since we need to pick one option explicitly, the answer is:

The graph with the correct plotted points is Option #1 or Option #3 (both are correct).

However, pick Option #1 if you are required to pick one.

Answer 2

Annabel wants to make banana bread for the bake sale. She went to the market to buy bananas, and she noticed fruit flies after she returned home with her produce. The number of fruit flies grows at an exponential rate modeled by the equation f(t)=8(2)t
, where f is the number of fruit flies after t days. Define an appropriate domain for the problem if Annabel bakes the banana bread 5 days after returning from the market.(1 point)
Responses

0≤t≤5
0 less than or equal to t less than or equal to 5

0≤f≤256
0 less than or equal to f less than or equal to 256

0≤f≤5
0 less than or equal to f less than or equal to 5

0≤t≤256

Answer 3

To define an appropriate domain for the problem involving the number of fruit flies, we consider that \( t \) represents the number of days after Annabel returns from the market. Since Annabel bakes the banana bread 5 days after returning, the relevant time period (domain) for this situation would be from day 0 (the day she returns from the market) to day 5 (the day she bakes).

Thus, the appropriate domain for \( t \) is:

0 ≤ t ≤ 5

In symbolic notation, it can also be expressed as:

0 ≤ t ≤ 5

So the correct response is:

0 ≤ t ≤ 5