Question
Use the table to answer the question.
x f(x)
0 3
1 3.6
2 4.32
3 5.18
4 ?
5 7.46
Find the missing value in the table for the exponential function f(x)=3(1.2)x
. Round your answer to two decimal places.
(1 point)
f(4)=
x f(x)
0 3
1 3.6
2 4.32
3 5.18
4 ?
5 7.46
Find the missing value in the table for the exponential function f(x)=3(1.2)x
. Round your answer to two decimal places.
(1 point)
f(4)=
Answers
GPT-4o mini
To find the missing value for \( f(4) \) using the given exponential function \( f(x) = 3(1.2)^x \), we can substitute \( x = 4 \) into the equation.
\[
f(4) = 3(1.2)^4
\]
Now, we need to calculate \( (1.2)^4 \):
\[
(1.2)^4 = 1.2 \times 1.2 \times 1.2 \times 1.2
\]
Calculating step-by-step:
1. \( 1.2 \times 1.2 = 1.44 \)
2. \( 1.44 \times 1.2 = 1.728 \)
3. \( 1.728 \times 1.2 = 2.0736 \)
Now we can use this result to find \( f(4) \):
\[
f(4) = 3 \times 2.0736 = 6.2208
\]
Finally, rounding to two decimal places, we have:
\[
f(4) \approx 6.22
\]
Thus, the missing value in the table is:
\[
\boxed{6.22}
\]
\[
f(4) = 3(1.2)^4
\]
Now, we need to calculate \( (1.2)^4 \):
\[
(1.2)^4 = 1.2 \times 1.2 \times 1.2 \times 1.2
\]
Calculating step-by-step:
1. \( 1.2 \times 1.2 = 1.44 \)
2. \( 1.44 \times 1.2 = 1.728 \)
3. \( 1.728 \times 1.2 = 2.0736 \)
Now we can use this result to find \( f(4) \):
\[
f(4) = 3 \times 2.0736 = 6.2208
\]
Finally, rounding to two decimal places, we have:
\[
f(4) \approx 6.22
\]
Thus, the missing value in the table is:
\[
\boxed{6.22}
\]
Use the table to answer the 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 #
.
Remaining Attempts : 3
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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 #
.
Remaining Attempts : 3
Skip to navigation