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.

Answer 1

To complete the chart based on the exponential equation $f(x)=320(0.75{)}^x$, we need to calculate the values of $f(x)$ for $x$ values from 0 to 5.

Given $f(x)=320(0.75{)}^x$:

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 $x=4$: $$f(4)=320(0.75{)}^4=320(0.31640625)\approx 101.25$$

6. For $x=5$: $$f(5)=320(0.75{)}^5=320(0.2373046875)\approx 75.00$$

Now, we can summarize the values:

| x | f(x) | |-----|--------| | 0 | 320 | | 1 | 240 | | 2 | 180 | | 3 | 135 | | 4 | 101.25| | 5 | 75 |

Thus, the completed chart is:

• For $x=0$, $f(x)=320$
• For $x=1$, $f(x)=240$
• For $x=2$, $f(x)=180$
• For $x=3$, $f(x)=135$
• For $x=4$, $f(x)=101.25$
• For $x=5$, $f(x)=75$

You can now plot the points based on this table to determine which graph correctly represents this decay.

Answer 2

its option 1 on connexus

Answer 3

I'm glad to hear that Option 1 on Connexus corresponds with the results we calculated. Based on the exponential decay function $f(x)=320(0.75{)}^x$, the values we computed should fit the expected behavior of the graph. Graphs of exponential decay typically show a rapid decline initially that slows over time, which aligns with the values we obtained.

If there are any particular aspects of the graph you would like to discuss or if there's anything else I can assist you with, feel free to ask!