Question
What number would be output when an input of 4 is evaluated using the rule shown in the image? Enter your response in the output box. (1 point)
Input 4 Rule multiply by 3, then add 1 () output
Input 4 Rule multiply by 3, then add 1 () output
Answers
GPT-4o mini
To find the output for an input of 4 using the rule provided (multiply by 3, then add 1), we can follow these steps:
1. Multiply the input (4) by 3:
\( 4 \times 3 = 12 \)
2. Add 1 to the result:
\( 12 + 1 = 13 \)
Therefore, the output is **13**.
1. Multiply the input (4) by 3:
\( 4 \times 3 = 12 \)
2. Add 1 to the result:
\( 12 + 1 = 13 \)
Therefore, the output is **13**.
Finally Some Answers
The number of bugs doubles every 4 days. If the bug population starts with 6 bugs, then the equation A(t)=6(2)^0.25t can represent the number of bugs. Find the value for A(8) .(1 point) The number of bugs after 8 days is
GPT-4o mini
To find the value of \( A(8) \) using the equation \( A(t) = 6(2)^{0.25t} \), we will substitute \( t = 8 \) into the equation.
1. Substitute \( t = 8 \):
\[
A(8) = 6(2)^{0.25 \times 8}
\]
2. Calculate \( 0.25 \times 8 \):
\[
0.25 \times 8 = 2
\]
3. Now replace the exponent in the equation:
\[
A(8) = 6(2)^{2}
\]
4. Calculate \( (2)^{2} \):
\[
(2)^{2} = 4
\]
5. Now multiply by 6:
\[
A(8) = 6 \times 4 = 24
\]
Therefore, the number of bugs after 8 days is **24**.
1. Substitute \( t = 8 \):
\[
A(8) = 6(2)^{0.25 \times 8}
\]
2. Calculate \( 0.25 \times 8 \):
\[
0.25 \times 8 = 2
\]
3. Now replace the exponent in the equation:
\[
A(8) = 6(2)^{2}
\]
4. Calculate \( (2)^{2} \):
\[
(2)^{2} = 4
\]
5. Now multiply by 6:
\[
A(8) = 6 \times 4 = 24
\]
Therefore, the number of bugs after 8 days is **24**.
Finally Some Answers
The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65h represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h , you have traveled. Find the distance left to get to Bloomsfield after 3 1/2 hours of traveling. Enter your response in decimal form.(1 point) The distance that you have left to travel is () miles.
GPT-4o mini
To find the distance left to get to Bloomsfield after traveling for \( 3.5 \) hours, we'll substitute \( h = 3.5 \) into the function \( D(h) = 440 - 65h \).
1. Substitute \( h = 3.5 \):
\[
D(3.5) = 440 - 65 \times 3.5
\]
2. Calculate \( 65 \times 3.5 \):
\[
65 \times 3.5 = 227.5
\]
3. Now, replace this value back into the equation:
\[
D(3.5) = 440 - 227.5
\]
4. Perform the subtraction:
\[
D(3.5) = 212.5
\]
Therefore, the distance left to travel to get to Bloomsfield after \( 3.5 \) hours is **212.5** miles.
1. Substitute \( h = 3.5 \):
\[
D(3.5) = 440 - 65 \times 3.5
\]
2. Calculate \( 65 \times 3.5 \):
\[
65 \times 3.5 = 227.5
\]
3. Now, replace this value back into the equation:
\[
D(3.5) = 440 - 227.5
\]
4. Perform the subtraction:
\[
D(3.5) = 212.5
\]
Therefore, the distance left to travel to get to Bloomsfield after \( 3.5 \) hours is **212.5** miles.