Create a sequence to show exponential growth where the population of 120 is doubling every day.(1 point)

Question

Responses

120, 240, 480 . . .
120, 240, 480 . . .

120, 360, 1,080 . . .
120, 360, 1,080 . . .

120, 60, 30 . . .
120, 60, 30 . . .

120, 240, 480, 360, 480 . . .

Answer 1

The correct sequence to show exponential growth where the population of 120 is doubling every day would be:

120, 240, 480, 960, 1920 . . .

However, from the provided options, the closest correct sequence is:

120, 240, 480 . . .

This option shows the population doubling as expected.

Answer 2

Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125. 10.71875 . . .
.(1 point)
Responses

y=21.5x
y equals Start Fraction 2 over 1.5 x End Fraction

y=2(1.75)x−1
y equals 2 left parenthesis 1.75 right parenthesis superscript x baseline

y=2+1.75x
y equals 2 plus 1.75 x

y=2(1.5)x

Answer 3

To find an accurate formula for the sequence \(2, 3.5, 6.125, 10.71875, \ldots\), we can analyze the pattern.

It seems that each term is multiplied by a common ratio which appears to be \(1.75\). Let's check this by calculating the next term based on the previous one:

• \(2 \times 1.75 = 3.5\)
• \(3.5 \times 1.75 = 6.125\)
• \(6.125 \times 1.75 = 10.71875\)

Given this pattern, the formula that fits this sequence is:

\[ y = 2(1.75)^{x-1} \]

Thus, the correct response is:

y = 2(1.75)^{x-1}

Answer 4

Use the image to answer the question.

A concave-up, increasing curve is plotted on a coordinate plane. The x-axis ranges from 0 to 4 in increments of 0.1 but labeled at 0.5 intervals. The y-axis ranges from 0 to 800 in increments of 50 but labeled at intervals of 200. The curve passes through 4 marked and labeled points.

Which of the following situations could describe the graph?

(1 point)
Responses

There are 200 cockroaches in a building, and the population triples every day.
There are 200 cockroaches in a building, and the population triples every day.

Niall rents a bike for $20 per hour.
Niall rents a bike for $20 per hour.

Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

Juveldy puts $20 in a high-yield savings account. His investment triples every year.

Answer 5

To determine which situation could describe the concave-up, increasing curve you described, we need to consider the nature of each scenario.

1. There are 200 cockroaches in a building, and the population triples every day.

   • This represents exponential growth and would result in a rapidly increasing curve that becomes very steep, likely leading to a curve that becomes concave down after a few days due to the nature of exponential growth.

2. Niall rents a bike for $20 per hour.

   • This situation results in a linear increase, as the cost increases by a constant rate every hour. The curve would not be concave up.

3. Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

   • This represents exponential growth as well (20% increase annually), resulting in a curve that could be concave up over time but will increase at a slower rate compared to situations with tripling.

4. Juveldy puts $20 in a high-yield savings account. His investment triples every year.

   • Similar to the cockroach population, tripling each year would lead to exponential growth and a curve that is steep and increases rapidly, likely also becoming concave down.

Given your description of the curve being concave up and increasing, the best response that fits is:

Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

This scenario describes an exponential growth that stays concave up as it appreciates by a consistent percentage each year.

Answer 6

Lori buys five goldfish for her tank. Her research shows that they will reproduce at a rate of 32 percent each month. Which statement discusses a key feature of the graph of this situation?(1 point)
Responses

The points on the graph will have a common ratio of 1.32.
The points on the graph will have a common ratio of 1.32.

The graph will begin with the point (1,5)
because Lori starts with five fish.
The graph will begin with the point left parenthesis 1 comma 5 right parenthesis because Lori starts with five fish.

The graph will have a constant rate of change.
The graph will have a constant rate of change.

The points on the graph will have a common ratio of 32.

Answer 7

To analyze the situation where Lori has five goldfish that reproduce at a rate of 32 percent each month, we can break down the key features of the graph of this scenario:

1. Common Ratio: Since the goldfish reproduce at a rate of 32 percent, the growth factor each month for the goldfish population can be calculated as \(1 + 0.32 = 1.32\). This indicates that the population will grow to 132% of its current size each month.

2. Starting Point: The initial number of goldfish is 5, which means the graph will start at the point representing this initial quantity of fish.

3. Constant Rate of Change: Since the population grows by a percentage (32%) each month, the rate of change is not constant; it increases as the population grows.

4. Common Ratio of 32: This statement is incorrect because the growth factor pertains to the 32% increase, not a common ratio of 32.

Based on this analysis, the correct statement that discusses a key feature of the graph of this situation is:

The points on the graph will have a common ratio of 1.32.

Answer 8

Use the image to answer the question.

A coordinate plane's axes range from 0 to 8 in 0.5-unit increments, but labeled at every 2-unit interval. A curve is plotted passing through four marked points.

What is the initial value of the sequence?

(1 point)
Responses

0
0

2
2

0.5
0.5

1

Answer 9

To determine the initial value of the sequence from the described coordinate plane, we need to look for the point on the graph where the curve starts, specifically along the y-axis (which typically represents the initial value when x = 0).

Since the axes range from 0 to 8 and are labeled at every 2-unit interval, the initial value corresponds to the y-coordinate where the curve intersects the y-axis.

Given your choices:

1. 0
2. 2
3. 0.5
4. 1

Without seeing the image, I cannot definitively identify which of these values is the initial value. However, if the curve starts at the y-axis (x = 0), you would check the point where it intersects to identify the correct response.

If you can determine where the curve intersects the y-axis or any marked points corresponding to the x-value of 0, that would give you the initial value. Based on typical behavior in these contexts, the initial value may often be small; you'll need to refer to the specific graph you have to make the final selection.

If the curve starts at 0 on the y-axis, then the answer would be 0. If it starts at another value like 2 or 1, select accordingly based on what you observe. If you have more information or a description of the curve's start, please share that for a more precise answer!