4. The table shows the predicted growth of particular bacterium after various numbers of hours. Write an explicit formula for the sequence of the numbers of bacterium
Hours (n) 1 2 3 4 5
Numbers of bacterium 22 44 66 88 110
an = 1/22 n
an = n +22
an = 22n +1
an = 22n
5. Suppouse you drop a tennis ball from a height of 6 feet. After the ball hits the floor it rebounds to 80% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.
4.8 feet
3.8 feet
1 feet
3.1 feet
9 answers
3.1 feet
he table shows the predicted growth of particular bacterium after various numbers of hours. Write an explicit formula for the sequence of the numbers of bacterium
Hours (n) 1 2 3 4 5
Numbers of bacterium 22 44 66 88 110
an = 1/22 n
an = n +22
an = 22n +1
an = 22n
Hours (n) 1 2 3 4 5
Numbers of bacterium 22 44 66 88 110
an = 1/22 n
an = n +22
an = 22n +1
an = 22n
an = 22n
The table shows the predicted growth of particular bacterium after various numbers of hours. Write an explicit formula for the sequence of the numbers of bacterium
Hours (n) 1 2 3 4 5
Numbers of bacterium 22 44 66 88 110
an = 1/22 n
an = n +22
an = 22n +1
an = 22n
show your work
Hours (n) 1 2 3 4 5
Numbers of bacterium 22 44 66 88 110
an = 1/22 n
an = n +22
an = 22n +1
an = 22n
show your work
To find the explicit formula for the sequence of the numbers of bacterium, we need to look for a pattern in the given sequence.
We can observe that the numbers of bacterium increase by 22 after every hour. So, the nth term of the sequence can be represented by:
an = 22n
Therefore, the explicit formula for the sequence of the numbers of bacterium is an = 22n.
We can observe that the numbers of bacterium increase by 22 after every hour. So, the nth term of the sequence can be represented by:
an = 22n
Therefore, the explicit formula for the sequence of the numbers of bacterium is an = 22n.
4. Suppouse you drop a tennis ball from a height of 6 feet. After the ball hits the floor it rebounds to 80% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.
4.8 feet
3.8 feet
1 feet
3.1 feet
4.8 feet
3.8 feet
1 feet
3.1 feet
To find the height of the ball after its third bounce, we need to first find the height it rebounds to after the second bounce, and then use that height to find the height after the third bounce.
After the first bounce, the ball rebounds to 80% of its previous height, which is 0.8 * 6 = 4.8 feet.
After the second bounce, the ball rebounds to 80% of 4.8 feet, which is 0.8 * 4.8 = 3.84 feet.
Finally, after the third bounce, the ball rebounds to 80% of 3.84 feet, which is 0.8 * 3.84 = 3.072 feet, rounded to the nearest tenth is 3.1 feet.
Therefore, the height of the ball after its third bounce is 3.1 feet.
After the first bounce, the ball rebounds to 80% of its previous height, which is 0.8 * 6 = 4.8 feet.
After the second bounce, the ball rebounds to 80% of 4.8 feet, which is 0.8 * 4.8 = 3.84 feet.
Finally, after the third bounce, the ball rebounds to 80% of 3.84 feet, which is 0.8 * 3.84 = 3.072 feet, rounded to the nearest tenth is 3.1 feet.
Therefore, the height of the ball after its third bounce is 3.1 feet.
what is the 12 term of the sequence 10, 6,2
-16
-24
-34
-38
-16
-24
-34
-38
To find the 12th term of the sequence 10, 6, 2, we need to identify the pattern of the sequence first. We can see that the sequence subtracts 4 successively to get to each term.
So, the first term is 10, the second term is 6 (which is 4 less than the previous term), and the third term is 2 (which is 4 less than the previous term). We can continue this pattern to get the rest of the sequence:
10, 6, 2, -2, -6, -10, -14, -18, -22, -26, -30, -34, ...
To find the 12th term, we can use the formula:
an = a1 + (n-1)*d
where an is the nth term, a1 is the first term, n is the number of the term we want to find, and d is the common difference.
So, for n = 12, we have:
a12 = 10 + (12-1)*(-4)
a12 = 10 - 44
a12 = -34
Therefore, the 12th term of the sequence 10, 6, 2 is -34. So, the answer is option (C) -34.
So, the first term is 10, the second term is 6 (which is 4 less than the previous term), and the third term is 2 (which is 4 less than the previous term). We can continue this pattern to get the rest of the sequence:
10, 6, 2, -2, -6, -10, -14, -18, -22, -26, -30, -34, ...
To find the 12th term, we can use the formula:
an = a1 + (n-1)*d
where an is the nth term, a1 is the first term, n is the number of the term we want to find, and d is the common difference.
So, for n = 12, we have:
a12 = 10 + (12-1)*(-4)
a12 = 10 - 44
a12 = -34
Therefore, the 12th term of the sequence 10, 6, 2 is -34. So, the answer is option (C) -34.